Chapter 4: Homework Questions
4-4 Refer to the table below. Given that 2 of the 198 subjects are randomly selected, complete parts (a) and (b). Group O A B AB Rh+ 71 47 16 17 Rh- 17 15 8 7 a. Assume that the selections are made with replacement. What is the probability that the 2 selected subjects are both group AB and type Rh Superscript plus? . 0074 (Round to four decimal places as needed.) b. Assume the selections are made without replacement. What is the probability that the 2 selected subjects are both group AB and type Rh Superscript plus? . 0070
.0074 .0070
4.2 Among respondents asked which is their favorite seat on a plane, 485 chose the window seat, 9 chose the middle seat, and 301 chose the aisle seat. What is the probability that a passenger prefers the middle seat? Is it unlikely for a passenger to prefer the middle seat? If so, why is the middle seat so unpopular? The probability that a passenger prefers the middle seat is . 011. (Round to three decimal places as needed.) Is it unlikely for a passenger to prefer the middle seat? A. No, because the probability that a passenger prefers the middle seat is greater than 0.05. B. No, because the probability that a passenger prefers the middle seat is less than 0.05. C. Yes, because the probability that a passenger prefers the middle seat is less than 0.05. D. Yes, because the probability that a passenger prefers the middle seat is greater than 0.05. If so, why is the middle seat so unpopular? A. Tickets for the middle seat are cheaper. B. The middle seat is more comfortable than window or aisle seats. C. The middle seat offers more opportunities for conversation with other passengers. D. The middle seat lacks an outside view, easy access to the aisle, and a passenger in the middle seat has passengers on both sides instead of on one side only. E. It is not true that the middle seat is unpopular.
.011 C D
4.2 A test for marijuana usage was tried on 194 subjects who did not use marijuana. The test result was wrong 5 times. a. Based on the available results, find the probability of a wrong test result for a person who does not use marijuana. b. Is it "unlikely" for the test to be wrong for those not using marijuana? Consider an event to be unlikely if its probability is less than or equal to 0.05. a. The probability that the test will be wrong is approximately . 026. (Type an integer or decimal rounded to three decimal places as needed.) b. Is it "unlikely" for the test to be wrong for those not using marijuana? Choose the correct answer below. Yes No
.026 Yes
4-4 The data in the following table summarize results from 129 pedestrian deaths that were caused by accidents. If three different deaths are randomly selected without replacement, find the probability that they all involved intoxicated drivers. (P)Intoxicated? Yes No (D)Intoxicated? Yes 23 26 No 44 36 The probability is . 052715. Is such an event unlikely? A. Yes, because its probability is less than 0.05. B. No, because its probability is less than 0.05. C. Yes, because its probability is greater than 0.05. D. No, because its probability is greater than 0.05.
.052715 D
4-4 The principle of redundancy is used when system reliability is improved through redundant or backup components. Assume that a student's alarm clock has a 6.7% daily failure rate. Complete parts (a) through (d) below. a. What is the probability that the student's alarm clock will not work on the morning of an important final exam? . 067 (Round to three decimal places as needed.) b. If the student has two such alarm clocks, what is the probability that they both fail on the morning of an important final exam? . 00449 (Round to five decimal places as needed.) c. What is the probability of not being awakened if the student uses three independent alarm clocks? . 00030 (Round to five decimal places as needed.) d. Do the second and third alarm clocks result in greatly improved reliability? A. Yes, because total malfunction would not be impossible, but it would be unlikely. B. No, because total malfunction would still not be unlikely. C. No, because the malfunction of both is equally or more likely than the malfunction of one. D. Yes, because you can always be certain that at least one alarm clock will work.
.067 .00449 .00030 A
4.2 In a certain weather forecast comma the chances of a thunderstorm are stated as "2 in 23." Express the indicated degree of likelihood as a probability value between 0 and 1 inclusive. The probability is . 087.
.087
4-3 Use the following results from a test for marijuana use, which is provided by a certain drug testing company. Among 148 subjects with positive test results, there are 22 false positive results; among 151 negative results, there are 5 false negative results. If one of the test subjects is randomly selected, find the probability of a false positive or false negative. (Hint: Construct a table.) What does the result suggest about the test's accuracy? The probability of a false positive or false negative is . 090. What does the result suggest about the test's accuracy? A. With an error rate of 0.910 (or 91.0%), the test appears to be highly accurate. B. With an error rate of 0.090 (or 9.0%), the test does not appear to be highly accurate. C. With an error rate of 0.090 (or 9.0%), the test appears to be highly accurate. D. With an error rate of 0.910 (or 91.0%), the test does not appear to be highly accurate.
.090 B
4-4 The data in the table below summarize results from 147 pedestrian deaths that were caused by accidents. If two different deaths are randomly selected without replacement, find the probability that they both involved intoxicated drivers. Is such an event unlikely? (P) Intoxicated? Yes NO (D)Intoxicated? YES 16 29 NO 48 54 The probability is . 094. Is such an event unlikely? A. Yes, because its probability is less than 0.05. B. No, because its probability is less than 0.05. C. Yes, because its probability is greater than 0.05. D. No, because its probability is greater than 0.05.
.094 D
4-5 The data represent the results for a test for a certain disease. Assume one individual from the group is randomly selected. Find the probability of getting someone who tests negative, given that he or she had the disease. The individual actually had the disease Yes No Positive 122 21 Negative 16 141 The probability is approximately . 116.
.116
4.2 In a certain instant lottery game comma the chance of a win is stated as 12%. Express the indicated degree of likelihood as a probability value between 0 and 1 inclusive. The probability is .12.
.12
4-5 The probability of a randomly selected car crashing during a year in a certain country is 0.0497. If a family has three cars, find the probability that at least one of them has a car crash during a year. Is there any reason why the probability might be wrong? The probability that at least one of them has a crash during the year is . 142. (Round to three decimal places as needed.) Is there a reason why the probability might be wrong? A. No, the three cars are representative of all cars in the country. B.No, one outcome does not have an effect on later trials. C.Yes, the three cars are not randomly selected. D.Yes, one outcome has an effect on later trials.
.142 C
4-3 The table below summarizes results from a study of people who refused to answer survey questions. If one of the subjects is randomly selected, what is the probability that the selected person refused to answer? Does the probability value suggest that refusals are a problem for pollsters? Age 18-21 22-29 30-39 40-49 50-59 Responded 71 253 243 134 136 Refused 14 23 36 29 38 60 and over 200 60 The probability that a randomly selected person refused to answer is . 162. Does the probability value suggest that refusals are a problem for pollsters? A. No, the refusal rate is below 10%. The sample will likely be representative of the population. B. Yes, the refusal rate is above 10%. This results in a sample size that is too small to be useful. C. Yes, the refusal rate is above 10%. This may suggest that the sample may not be representative of the population. D. No, the refusal rate is below 10%. This ensures that a suitable number of people were sampled.
.162 C
4-3 A research center poll showed that 83% of people believe that it is morally wrong to not report all income on tax returns. What is the probability that someone does not have this belief? The probability that someone does not believe that it is morally wrong to not report all income on tax returns is . 17.
.17
4.2 Refer to the sample data for pre-employment drug screening shown below. If one of the subjects is randomly selected, what is the probability that the test result is a false positive? Who would suffer from a false positive result? Why? Pre-Employment Drug Screening Results Positive test result Negative test result Drug Use Is Indicated Drug Use Is Not Indicated Subject Uses Drugs Subject Is Not a Drug User 39 11 19 30 The probability of a false positive test result is . 192. (Round to three decimal places as needed.) Who would suffer from a false positive result? Why? A. The employer would suffer because the person tested would be suspected of using drugs when in reality he or she does not use drugs. B. The employer would suffer because the person tested would not be suspected of using drugs when in reality he or she does use drugs. C. The person tested would suffer because he or she would be suspected of using drugs when in reality he or she does not use drugs. D. The person tested would suffer because he or she would not be suspected of using drugs when in reality he or she does use drugs.
.192 C
4-5 The table below displays results from experiments with polygraph instruments. Find Upper P left parenthesis subject lied | negative test result right parenthesis . Compare this result with the probability of selecting a subject with a negative test result, given that the subject lied. Are Upper P left parenthesis subject lied | negative test result right parenthesis and Upper P left parenthesis negative test result | subject lied right parenthesis equal? Did the Subject Actually Lie? No (Did Not Lie) Yes (Lied) Pos.test results 18 40 Neg.test results 34 9 P(subject lied | negative test result)equals .209 Find the probability of selecting a subject with a negative test result, given that the subject lied. Upper P left parenthesis negative test result | subject lied right parenthesisequals . 184 (Round to three decimal places as needed.) Compare the two values. Are they equal? No Yes
.209 .184 No
4-4 With one method of a procedure called acceptance sampling, a sample of items is randomly selected without replacement and the entire batch is accepted if every item in the sample is okay. A company has just manufactured 546 CDs, and 212 are defective. If 3 of these CDs are randomly selected for testing, what is the probability that the entire batch will be accepted? Does this outcome suggest that the entire batch consists of good CDs? Why or why not? If 3 of these CDs are randomly selected for testing, what is the probability that the entire batch will be accepted? The probability that the whole batch is accepted is . 229. (Round to three decimal places as needed.) Does the result in (a) suggest that the entire batch consists of good CDs? Why or why not? A. No, because the sample will always consist of good CDs. B. Yes, because if all three CDs in the sample are good then the entire batch must be good. C. No, because only a probability of 1 would indicate the entire batch consists of good CDs. D. Yes, because it is not unlikely that the batch will be accepted.
.229 C
4.2 For a certain casino slot machine comma the odds in favor of a win are given as 29 to 71. Express the indicated degree of likelihood as a probability value between 0 and 1 inclusive. The probability is . 29.
.29
4.2 To the right are the outcomes that are possible when a couple has three children. Refer to that list, and find the probability of each event. a. Among three children, there are exactly 2 boys. b. Among three children, there are exactly 0 girls. c. Among three children, there is exactly 1 boy. 1st 2nd 3rd boyminusboyminusboy boyminusboyminusgirl boyminusgirlminusboy boyminusgirlminusgirl girlminusboyminusboy girlminusboyminusgirl girlminusgirlminusboy girlminusgirlminusgirl a. What is the probability of exactly 2 boys out of three children? . 375 (Type an integer or a simplified fraction.) b. What is the probability of exactly 0 girls out of three children? . 125 (Type an integer or a simplified fraction.) c. What is the probability of exactly 1 boy out of three children? . 375 (Type an integer or a simplified fraction.)
.375 .125 .375
4-3 The following data lists the number of correct and wrong dosage amounts calculated by 30 physicians. In a research experiment, a group of 13 physicians was given bottles of epinephrine labeled with a concentration of "1 milligram in 1 milliliter solution," and another group of 17 physicians was given bottles labeled with a ratio of "1 milliliter of a 1:1000 solution." If one of the physicians is randomly selected, what is the probability of getting one who calculated the dose correctly? Is that probability as high as it should be? Correct Dosage Calculation Wrong Dosage Calculation Concentration Label ("1 milligram in 1 milliliter solution") 11 2 Ratio Label 2 15 ("1 milliliter of a 1:1000 solution") P(physician calculated the dose correctly)equals .433 (Round to three decimal places as needed.) Is that probability as high as it should be? A. No. A large sample should result in a small probability. B. No. One would want this probability to be very high. C. Yes. The probability seems sufficiently high. D. Yes. A large sample should result in a high probability.
.433 B
4.2 Refer to the sample data for polygraph tests shown below. If one of the test subjects is randomly selected, what is the probability that the subject is not lying? Is the result close to the probability of 0.393 for a negative test result? Did the Subject Actually Lie? No (Did Not Lie) Yes (Lied) Positive test results 10 44 Negative test results 29 6 The probability that a randomly selected polygraph test subject was not lying is . 438. (Type an integer or decimal rounded to three decimal places as needed.) Is the result close to the probability, rounded to three decimal places, of 0.393 for a negative test result? A. Yes, because there is less than a 0.050 absolute difference between the probability of a true response and the probability of a negative test result. B. No, because there is less than a 0.050 absolute difference between the probability of a true response and the probability of a negative test result. C. Yes, because there is more than a 0.050 absolute difference between the probability of a true response and the probability of a negative test result. D. No, because there is more than a 0.050 absolute difference between the probability of a true response and the probability of a negative test result.
.438 A
4-3 The following data summarizes results from 1021 pedestrian deaths that were caused by accidents. If one of the pedestrian deaths is randomly selected, find the probability that the pedestrian was intoxicated or the driver was intoxicated. Pedestrian (p)intoxicated (p)not intoxicated (d) intoxicated 97 74 (d)not intoxicated 284 566 P(pedestrian was intoxicated or driver was intoxicated)equals . 446
.446
4.2 In a test of a gender-selection technique, results consisted of 239 baby girls and 257 baby boys. Based on this result, what is the probability of a girl born to a couple using this technique? Does it appear that the technique is effective in increasing the likelihood that a baby will be a girl? The probability that a girl will be born using this technique is approximately . 482. (Type an integer or decimal rounded to three decimal places as needed.) Does the technique appear effective in improving the likelihood of having a girl baby? No Yes
.482 No
4-3 The following data lists the number of correct and wrong dosage amounts calculated by 27 physicians. In a research experiment, a group of 12 physicians was given bottles of epinephrine labeled with a concentration of "1 milligram in 1 milliliter solution," and another group of 15 physicians was given bottles labeled with a ratio of "1 milliliter of a 1:1000 solution." If one of the physicians is randomly selected, find the probability of getting one who made a correct dosage calculation or was given the bottle with a concentration label. Correct Dosage Calculation Wrong Dosage Calculation Concentration Label ("1 milligram in 1 milliliter solution") 10 2 Ratio Label 2 13 ("1 milliliter of a 1:1000 solution") P(physician made a correct dosage calculation or was given the bottle with a concentration label) equals. 519
.519
4-3 Use the following results from a test for marijuana use, which is provided by a certain drug testing company. Among 142 subjects with positive test results, there are 24 false positive results; among 151 negative results, there are 3 false negative results. If one of the test subjects is randomly selected, find the probability that the subject tested negative or did not use marijuana. (Hint: Construct a table.) The probability that a randomly selected subject tested negative or did not use marijuana is . 597.
.597
4-5 The table below displays results from experiments with polygraph instruments. Find the positive predictive value for the test. That is, find the probability that the subject lied, given that the test yields a positive result. Did the Subject Actually Lie? No (Did Not Lie) Yes (Lied) Pos.test results 18 44 Neg. test results 32 10 The probability is . 710.
.710
4-5 The accompanying table displays results from experiments with polygraph instruments. a. Find Upper P left parenthesis subject told the truth | negative test result right parenthesis . b. Find Upper P left parenthesis negative test result | subject told the truth right parenthesis. c. Compare the results from parts a. and b. Are they equal? Did the Subject Actually Lie? No (Did Not Lie) Yes (Lied) Pos.test results 10 43 Neg. test results 33 9 a. Upper P left parenthesis subject told the truth | negative test result right parenthesis equals . 786 b. Find the probability of selecting a subject with a negative test result, given that the subject told the truth. Upper P left parenthesis negative test result | subject told the truth right parenthesisequals . 767 c. Compare the two values. Are they equal? Yes No
.786 .767 No
4.2 Ten of the 50 digital video recorders (DVRs) in an inventory are known to be defective. What is the probability you randomly select an item that is not defective? The probability is .8.
.8
4-3 The following data lists the number of correct and wrong dosage amounts calculated by 29 physicians. In a research experiment, a group of 14 physicians was given bottles of epinephrine labeled with a concentration of "1 milligram in 1 milliliter solution," and another group of 15 physicians was given bottles labeled with a ratio of "1 milliliter of a 1:1000 solution." Complete parts (a) through (c) below. Correct Dosage Calculation Wrong Dosage Calculation Concentration Label ("1 milligram in 1 milliliter solution") 12 2 Ratio Label 4 11 ("1 milliliter of a 1:1000 solution") a. For the physicians given the bottles labeled with a concentration, find the percentage of correct dosage calculations, and then express it as a probability. The probability of a correct dosage calculation given the bottle is labeled with a concentration is . 857. b. For the physicians given the bottles labeled with a ratio, find the percentage of correct dosage calculations, and then express it as a probability. The probability of a correct dosage calculation given the bottle is labeled with a ratio is . 267. c. Does it appear that either group did better? What does the result suggest about drug labels? It appears that _________ performed better because the probability of a correct dosage calculation for the bottles labeled with a concentration is _________the probability of a correct dosage calculation for the bottles labeled with a ratio. This result suggests that ______________.
.857 - the group given the labels with concentrations - much greater than - labels with concentrations are much better than labels with ratios
4-4 A tire company produced a batch of 6 comma 900 tires that includes exactly 260 that are defective. a. If 4 tires are randomly selected for installation on a car, what is the probability that they are all good? b. If 100 tires are randomly selected for shipment to an outlet, what is the probability that they are all good? Should this outlet plan to deal with defective tires returned by consumers? a. If 4 tires are randomly selected for installation on a car, what is the probability that they are all good?. 858 (Round to three decimal places as needed.) b. If 100 tires are randomly selected for shipment to an outlet what is the probability that they are all good? . 021 (Round to three decimal places as needed.) Should this outlet plan to deal with defective tires returned by consumers? A. No, because there is a very small chance that all 100 tires are good. B. Yes, because there is a very small chance that all 100 tires are good. C. No, because there is a very large chance that all 100 tires are good. D. Yes, because there is a very large chance that all 100 tires are good.
.858 .021 B
4.2 Among 300 randomly selected drivers in the 16 minus 18 age bracket, 259 were in a car crash in the last year. If a driver in that age bracket is randomly selected, what is the approximate probability that he or she will be in a car crash during the next year? Is it unlikely for a driver in that age bracket to be involved in a car crash during a year? Is the resulting value high enough to be of concern to those in the 16 minus 18 age bracket? Consider an event to be "unlikely" if its probability is less than or equal to 0.05. The probability that a randomly selected person in the 16 minus 18 age bracket will be in a car crash this year is approximately . 863. (Type an integer or decimal rounded to the nearest thousandth as needed.) Would it be unlikely for a driver in that age bracket to be involved in a car crash this year? Yes No Is the probability high enough to be of concern to those in the 16 minus 18 age bracket? Yes No
.863 No Yes
4-4 In a market research survey of 2486 motorists, 298 said that they made an obscene gesture in the previous month. Complete parts (a) and (b) below. a. If 1 of the surveyed motorists is randomly selected, what is the probability that this motorist did not make an obscene gesture in the previous month? The probability is . 8801. (Round to four decimal places as needed.) b. If 30 of the surveyed motorists are randomly selected without replacement, what is the probability that none of them made an obscene gesture in the previous month? Should the 5% guideline be applied in this case? Select the correct choice below and fill in the answer box within your choice. (Round to four decimal places as needed.) A. The probability is . 0217. The 5% guideline should be applied in this case. B. The probability is nothing. The 5% guideline should not be applied in this case.
.8801 A .0217
4-3 The table below summarizes results from a study of people who refused to answer survey questions. A market researcher is interested in responses, especially from those between the ages of 22 and 39. Find the probability that a selected subject responds or is between the ages of 22 and 39. Age 18-21 22-29 30-39 40-49 50-59 60 and over Responded 77 259 249 140 142 206 Refused 11 20 33 26 35 57 The probability that the subject responded or is between the ages of 22 and 39 is . 897.
.897
4.2 In a genetics experiment on peas, one sample of offspring contained 383 green peas and 31 yellow peas. Based on those results, estimate the probability of getting an offspring pea that is green. Is the result reasonably close to the value of 3 divided by 4 that was expected? The probability of getting a green pea is approximately . 925. (Type an integer or decimal rounded to three decimal places as needed.) Is this probability reasonably close to 3 divided by 4? Choose the correct answer below. Yes, it is reasonably close. No, it is not reasonably close.
.925 No
4-3 Pollsters are concerned about declining levels of cooperation among persons contacted in surveys. A pollster contacts 84 people in the 18-21 age bracket and finds that 59 of them respond and 25 refuse to respond. When 293 people in the 22-29 age bracket are contacted, 275 respond and 18 refuse to respond. Suppose that one of the 377 people is randomly selected. Find the probability of getting someone in the 22 dash 29 age bracket or someone who responded. P(person is in the 22 dash 29 age bracket or responded)equals . 934
.934
4-5 In a certain country, the true probability of a baby being a girl is 0.484. Among the next seven randomly selected births in the country, what is the probability that at least one of them is a boy? The probability is . 994.
.994
4-3 The following data summarizes results from 1000 pre-employment drug screening tests. If one of the test subjects is randomly selected, find the probability that the subject had a positive test result or a negative test result. Pos. Test Result Neg. Test Result Subject Uses Drugs 92 4 Subject Isn't a Drug User 86 818 P(subject had a positive test result or a negative test result)equals 1
1
4.2 You are certain to get a number or a face card when selecting cards from a shuffled deck. Express the indicated degree of likelihood as a probability value between 0 and 1 inclusive. The probability is 1.
1
4-5 Identical twins come from a single egg that split into two embryos, and fraternal twins are from separate fertilized eggs. Also, identical twins must be of the same sex and the sexes are equally likely, and sexes of fraternal twins are equally likely. If a pregnant woman is told that she will give birth to fraternal twins, what is the probability that she will have one child of each sex? Use the data table below to find the probability. Sexes of Twins b/b b/g g/b g/g Identical Twins 6 0 0 6 Fraternal Twins 2 2 2 2 The probability is 1/2
1/2
4-5 Find the probability of a couple having a baby girl when their fifth child is born, given that the first four children were all girls. Assume boys and girls are equally likely. Is the result the same as the probability of getting all girls among five children? The probability is 1/2 Is this result the same as the probability of getting all girls among five children? A. Yes. The events are all independent. B. No. The second event involves more possible outcomes. C. Yes. The final result in each case is the same. D. No. The two events are complements.
1/2 B
4-6 A presidential candidate plans to begin her campaign by visiting the capitals in 4 of 40 states. What is the probability that she selects the route of four specific capitals? Is it practical to list all of the different possible routes in order to select the one that is best? P(she selects the route of four specific capitals)equals 1/2193360 Is it practical to list all of the different possible routes in order to select the one that is best? A. Yes, it is practical to list all of the different possible routes because the number of possible permutations is very small. B. No, it is not practical to list all of the different possible routes because the number of possible permutations is very small. C. Yes, it is practical to list all of the different possible routes because the number of possible permutations is very large. D. No, it is not practical to list all of the different possible routes because the number of possible permutations is very large.
1/2193360 D
4-6 Select the six winning numbers from 1, 2, . . . , 26. (In any order. No repeats.) P(winning)equals 1/230230
1/230230
4-6 Winning the jackpot in a particular lottery requires that you select the correct five numbers between 1 and 40 and, in a separate drawing, you must also select the correct single number between 1 and 51. Find the probability of winning the jackpot. The probability of winning the jackpot is 1/33558408
1/33558408
4-6 If you know the names of the remaining ten students in the spelling bee, what is the probability of randomly selecting an order and getting the order that is used in the spelling bee? P(selecting the correct spelling bee order)equals 1/3628800
1/3628800
4-6 Winning the jackpot in a particular lottery requires that you select the correct two numbers between 1 and 43 and, in a separate drawing, you must also select the correct single number between 1 and 43. Find the probability of winning the jackpot. The probability of winning the jackpot is 1/38829
1/38829
4-4 Assume that a company hires employees on the different business days of the month left parenthesis Assume 20 business days in a month right parenthesis nbspwith equal likelihood. Complete parts (a) through (c) below. a. If two different employees are randomly selected, what is the probability that they were both hired on the last business day of the month? The probability is 1/400 b. If two different employees are randomly selected, what is the probability that they were both hired on the same ordered day of the business month? The probability is 1/20 c. What is the probability that 4 people in the same department were all hired on the same ordered day of the business month? Is such an event unlikely? The probability is 1/8000 Is such an event unlikely? A. Yes, because the probability that all 4 people were hired on the same ordered day of thenbsp business month is less than or equal to 0.05. B. Yes, because the probability that all 4 people were hired on the same ordered day of thenbsp business month is greater than 0.05. C. No, because the probability that all 4 people were hired on the same ordered day of thenbsp business month is less than or equal to 0.05. D. No, because the probability that all 4 people were hired on the same ordered day of thenbsp business month is greater than 0.05.
1/400 1/20 1/8000 A
4-6 When eight basketball players are about to have a free-throw competition, they often draw names out of a hat to randomly select the order in which they shoot. What is the probability that they shoot free throws in alphabetical order? Assume each player has a different name. P(shoot free throws in alphabetical order)equals 1/40320
1/40320
4-6 In a lottery game, the jackpot is won by selecting four different whole numbers from 1 through 35 and getting the same four numbers (in any order) that are later drawn. In the Pick 3 game, you win a straight bet by selecting three digits (with repetition allowed), each one from 0 to 9, and getting the same three digits in the exact order they are later drawn. The Pick 3 game returns $500 for a winning $1 ticket. Complete parts (a) through (c) below. a. In a lottery game, the jackpot is won by selecting four different whole numbers from 1 through 35 and getting the same four numbers (in any order) that are later drawn. What is the probability of winning a jackpot in this game? P(winning a jackpot in this game)equals 1/52360 b. In the Pick 3 game, you win a straight bet by selecting three digits (with repetition allowed), each one from 0 to 9, and getting the same three digits in the exact order they are later drawn. What is the probability of winning this game? P(winning the Pick 3 game)equals 1/1000 c. The Pick 3 game returns $500 for a winning $1 ticket. What should be the return if the lottery organization were to run this game for no profit? $1000
1/52360 1/1000 $1000
4-6 A fan of country music plans to make a custom CD with 11 of her 27 favorite songs. How many different combinations of 11 songs are possible? Is it practical to make a different CD for each possible combination? How many different combinations of 11 songs are possible? 13037895 Is it practical to make a different CD for each possible combination? A. No, it is not practical to make a different CD for each possible combination because the number of possible combinations is very small. B. Yes, it is practical to make a different CD for each possible combination because the number of possible combinations is very small. C. No, it is not practical to make a different CD for each possible combination because the number of possible combinations is very large. D. Yes, it is practical to make a different CD for each possible combination because the number of possible combinations is very large.
13037895 C
4-5 If a couple plans to have 8 children, what is the probability that there will be at least one girl? Assume boys and girls are equally likely. Is that probability high enough for the couple to be very confident that they will get at least one girl in 8 children? The probability is 255/256 Can the couple be very confident that they will have at least one girl? A. Yes because the probability is close to 0. B. No because the probability is close to 1. C. Yes because the probability is close to 1. D. No because the probability is close to 0.
255/256 C
4-3 Use the following results from a test for marijuana use, which is provided by a certain drug testing company. Among 143 subjects with positive test results, there are 29 false positive results. Among 151 negative results, there are 4 false negative results. Complete parts (a) through (c). (Hint: Construct a table.) a. How many subjects were included in the study? The total number of subjects in the study was 294. b. How many subjects did not use marijuana? A total of 176 subjects did not use marijuana. c. What is the probability that a randomly selected subject did not use marijuana? The probability that a randomly selected subject did not use marijuana is . 599.
294 176 .599
4-6 When testing for current in a cable with eleven color-coded wires, the author used a meter to test five wires at a time. How many different tests are required for every possible pairing of five wires? The number of tests required is 462.
462
4-6 Many newspapers carry a certain puzzle in which the reader must unscramble letters to form words. How many ways can the letters of RTLIOSN be arranged? Identify the correct unscrambling, then determine the probability of getting that result by randomly selecting one arrangement of the given letters. How many ways can the letters of RTLIOSN be arranged? 5040 What is the correct unscrambling of RTLIOSN? A. NILTORS B. STRONIL C. TRILONS D. NOSTRIL What is the probability of coming up with the correct unscrambling through random letter selection? 1/5040
5040 D 1/5040
4-6 A corporation must appoint a president, chief executive officer (CEO), chief operating officer (COO), and chief financial officer (CFO). It must also appoint a planning committee with four different members. There are 17 qualified candidates, and officers can also serve on the committee. Complete parts (a) through (c) below. a. How many different ways can the officers be appointed? There are 57120 different ways to appoint the officers. b. How many different ways can the committee be appointed? There are 2380 different ways to appoint the committee. c. What is the probability of randomly selecting the committee members and getting the four youngest of the qualified candidates? P(getting the four youngest of the qualified candidates)equals 1/2380
57120 2380 1/2380
4-6 A thief steals an ATM card and must randomly guess the correct five-digit pin code from a 9-key keypad. Repetition of digits is allowed. What is the probability of a correct guess on the first try? The number of possible codes is 59049. The probability that the correct code is given on the first try is 1/59049
59049 1/59049
4-5 Identical twins come from a single egg that split into two embryos, and fraternal twins are from separate fertilized eggs. Also, identical twins must be of the same sex and the sexes are equally likely, and sexes of fraternal twins are equally likely. Use the data table to complete parts (a) and (b) below. Sexes of Twins b/b b/g g/b g/g Identical Twins 7 0 0 7 Fraternal Twins 8 8 8 8 a. After having a sonogram, a pregnant woman learns that she will have twins. What is the probability that she will have identical twins? The probability is 7/23 b. After studying the sonogram more closely, the physician tells the pregnant woman that she will give birth to twin boys. What is the probability that she will have identical twins? That is, find the probability of identical twins given that the twins consist of two boys. The probability is 7/15
7/23 7/15
4-3 What is wrong with the expression Upper P left parenthesis Upper A right parenthesis plus Upper P left parenthesis Upper A overbar right parenthesis equals 0.5? A. Based on the rule of complements, the sum of P(A) and Upper P left parenthesis Upper A overbar right parenthesis must always be 1, so that sum cannot be 0.5. B. Based on the rule of complements, the sum of P(A) and Upper P left parenthesis Upper A overbar right parenthesis must always be 0, so that sum cannot be 0.5. C. Based on the rule of complements, the sum of P(A) and Upper P left parenthesis Upper A overbar right parenthesis must always be Upper P left parenthesis Upper A overbar right parenthesis. D. Based on the rule of complements, the sum of P(A) and Upper P left parenthesis Upper A overbar right parenthesis must always be P(A).
A
4-6 Which of the following is NOT a requirement of the Combinations Rule, nCr=n!/r!(n-r)! , for items that are all different? Choose the correct answer below. A. That order is taken into account (consider rearrangements of the same items to be different sequences). B. That there be n different items available. C. That r of the n items are selected (without replacement). D. That order is not taken into account (consider rearrangements of the same items to be the same).
A
4-6 Which of the following is NOT a requirement of the Permutations Rule, nPr=n!/(n-r)!, for items that are all different? Choose the correct answer below. A. Order is not taken into account (rearrangements of the same items are considered to be the same). B. Order is taken into account (rearrangements of the same items are considered to be different). C. There are n different items available. D. Exactly r of the n items are selected (without replacement).
A
4-4 For the given pair of events A and B, complete parts (a) and (b) below. A: When a page is randomly selected and ripped from a 16-page document and destroyed, it is page 3. B: When a different page is randomly selected and ripped from the document, it is page 7. a. Determine whether events A and B are independent or dependent. (If two events are technically dependent but can be treated as if they are independent according to the 5% guideline, consider them to be independent.) b. Find P(A and B), the probability that events A and B both occur. a. Choose the correct answer below. A. The two events are dependent because the occurrence of one affects the probability of the occurrence of the other. B. The two events are dependent because the occurrence of one does not affect the probability of the occurrence of the other. C. The two events are independent because the 5% guideline indicates that they should be treated as independent. D. The two events are independent because the occurrence of one does not affect the probability of the occurrence of the other. b. The probability that events A and B both occur is . 0042.
A .0042
4-6 A combination lock uses three numbers between 1 and 68 with repetition, and they must be selected in the correct sequence. Which of the five counting rules is used to find that number? How many different "combinations" are possible? Is the name of "combination lock" appropriate? If not, what other name would be better? Which of the five counting rules is used to find that number? A. Fundamental counting rule B. Combinations rule C. Permutations rule (when all of the items are different) D. Factorial rule E. Permutations rule (when some items are identical to others) How many different "combinations" are possible? The number of different "combinations" is 314432. (Type a whole number.) Is the name of "combination lock" appropriate? If not, what other name would be better? A. Yes. The name "combination lock" is appropriate. B. No. The name "number lock" is more appropriate because "fundamental counting rule lock" is awkward. C. No. The name "permutation lock" is more appropriate. D. No. The name "factorial lock" is more appropriate.
A 314432 B
4-5 The conditional probability of B given A can be found by _______. Choose the correct answer below. A. multiplying P(A) times P(B) B. assuming that event A has occurred, and then calculating the probability that event B will occur C. assuming that event B has occurred, and then calculating the probability that event A will occur D. adding P(A) and P(B)
B
4-5 When 15 computers are shipped, at least one of them is free of defects. A. None of them are defective B. All of them are defective C. More than one of them are defective D. All of them are free of defects
B
4-5 When seven cameras are received, none of them are defective. A. More than one of them are free of defects B. At least one of them is defective C. None of them are free of defects D. All of them are defective
B
4-3 In a computer instant messaging survey, respondents were asked to choose the most fun way to flirt, and it found that P(D)equals0.670, where D is directly in person. If someone is randomly selected, what does Upper P left parenthesis Upper D overbar right parenthesis represent, and what is its value? What does Upper P left parenthesis Upper D overbar right parenthesis represent? A. Upper P left parenthesis Upper D overbar right parenthesis is the probability of randomly selecting someone who did not participate in the survey. B. Upper P left parenthesis Upper D overbar right parenthesis is the probability of randomly selecting someone who does not choose a direct in-person encounter as the most fun way to flirt. C. Upper P left parenthesis Upper D overbar right parenthesis is the probability of randomly selecting someone who chooses a direct in-person encounter as the most fun way to flirt. D. Upper P left parenthesis Upper D overbar right parenthesis is the probability of randomly selecting someone who did not have a preference in regards to the most fun way to flirt. Upper P left (Upper D overbar right) equals. 33
B .33
4.2 Assume that 1300 births are randomly selected and exactly 644 of the births are girls. Use subjective judgment to determine whether the given outcome is unlikely, and also determine whether it is unusual in the sense that the result is far from what is typically expected. Determine whether exactly 644 girls out of 1300 randomly selected births is unlikely. A. It is not unlikely because 644 is about half of 1300. B. It is unlikely because the probability of this particular outcome is very small, considering all of the other possible outcomes. C. It is unlikely because it is not 650 as expected. D. It is not unlikely because girls are slightly less common than boys. Determine whether exactly 644 girls out of 1300 randomly selected births is unusual. A. It is not unusual because 644 is about the number of girls expected. B. It is unusual because girls are more common than boys. C. It is not unusual because 644 girls out of 1300 births is the only possible outcome. D. It is unusual because it is not 650 as expected.
B A
4.2 Assume that 1300 births are randomly selected and exactly 322 of the births are girls. Use subjective judgment to determine whether the given outcome is unlikely, and also determine whether it is unusual in the sense that the result is far from what is typically expected. Determine whether exactly 322 girls out of 1300 randomly selected births is unlikely. A. It is unlikely because it is not 650 as expected. B. It is unlikely because there are many other possible outcomes that have similar or higher probabilities. C. It is not unlikely because 322 is about one quarter of 1300. D. It is not unlikely because girls are slightly less common than boys. Determine whether exactly 322 girls out of 1300 randomly selected births is unusual. A. It is unusual because girls are much more common than boys. B. It is not unusual because 322 girls out of 1300 births is the only possible outcome. C. It is not unusual because 322 is about the number of girls expected.. D. It is unusual because it is not about 650 as expected.
B D
4-4 What does P(B|A) represent? Choose the correct answer below. A. The probability of event A occurring after it is assumed that event B has already occurred B. The probability of event A or event B or both occurring C. The probability of event B occurring after it is assumed that event A has already occurred D. The probability of event A and event B both occurring
C
4-4 Consider a bag that contains 216 coins of which 6 are rare Indian pennies. For the given pair of events A and B, complete parts (a) and (b) below. A: When one of the 216 coins is randomly selected, it is one of the 6 Indian pennies. B: When another one of the 216 coins is randomly selected (with replacement), it is also one of the 6 Indian pennies. a. Determine whether events A and B are independent or dependent. b. Find P(A and B), the probability that events A and B both occur. a. Choose the correct answer below. A. The two events are dependent because the 5% guideline indicates that they may be treated as dependent. B. The two events are independent because the 5% guideline indicates that they may be treated as independent. C. The two events are independent because the occurrence of one does not affect the probability of the occurrence of the other. D. The two events are dependent because the occurrence of one affects the probability of the occurrence of the other. b. The probability that events A and B both occur is . 000772.
C .000772
4.2 If A denotes some event, what does Upper A overbar denote? If P(A)equals0.997, what is the value of P(Upper A overbar)? If P(A)equals0.997, is Upper A overbar unlikely? What does Upper A overbar denote? A. Event Upper A overbar is always unlikely. B. Events A and Upper A overbar share all outcomes. C. Event Upper A overbar denotes the complement of event A, meaning that Upper A overbar consists of all outcomes in which event A does not occur. Your answer is correct.D. Event Upper A overbar denotes the complement of event A, meaning that Upper A overbar and A share some but not all outcomes. If P(A)equals0.997, what is the value of P(Upper A overbar)? P(Upper A overbar)equals . 003 (Type an integer or a decimal.) If P(A)equals0.997, is Upper A overbar unlikely?
C .003 Yes
4-4 For the given pair of events A and B, complete parts (a) and (b) below. A: A marble is randomly selected from a bag containing 17 marbles consisting of 1 red, 10 blue, and 6 green marbles. The selected marble is one of the green marbles. B: A second marble is selected and it is the 1 red marble in the bag. a. Determine whether events A and B are independent or dependent. (If two events are technically dependent but can be treated as if they are independent according to the 5% guideline, consider them to be independent.) b. Find P(A and B), the probability that events A and B both occur. a. Choose the correct answer below. A. The two events are dependent because the occurrence of one affects the probability of the occurrence of the other and the 5% guideline can be applied in this case. B. The two events are independent because the 5% guideline can be applied in this case. C. The two events are dependent because the occurrence of one affects the probability of the occurrence of the other and the 5% guideline cannot be applied in this case. D. The two events are independent because the occurrence of one does not affect the probability of the occurrence of the other. b. The probability that events A and B both occur is . 0221.
C .0221
4-4 The accompanying table contains the results from experiments with a polygraph instrument. Find the probabilities of the events in parts (a) and (b) below. Are these events unlikely? No (didnt lie) Yes(lied) Pos(subj lied) 5 (falsepos)27(trneg) Neg (subj didnot lie) 47(trneg)17(falseneg) a. Four of the test subjects are randomly selected with replacement, and they all had true negative test results. b. Four of the test subjects are randomly selected without replacement, and they all had true negative test results. LOADING... Click on the icon to view the data table. a. The probability that all four test subjects had a true negative test result when they are randomly selected with replacement is . 057. Is such an event unlikely? A. No, because the probability of the event is less than 0.05. B. Yes, because the probability of the event is less than 0.05. C. No, because the probability of the event is greater than 0.05. D. Yes, because the probability of the event is greater than 0.05. b. The probability that all four test subjects had a true negative test result when they are randomly selected without replacement is . 054.
C .054 B
4.2 Each of two parents has the genotype blue divided by brown, which consists of the pair of alleles that determine eye color, and each parent contributes one of those alleles to a child. Assume that if the child has at least one blue allele, that color will dominate and the child's eye color will be blue. a. List the different possible outcomes. Assume that these outcomes are equally likely. b. What is the probability that a child of these parents will have the brown divided by brown genotype? c. What is the probability that the child will have blue eye color? a. List the possible outcomes. A. blue divided by blue comma blue divided by brown comma and brown divided by brown B. blue divided by blue and brown divided by brown C. blue divided by blue comma blue divided by brown comma brown divided by blue comma and brown divided by brown D. blue divided by brown and brown divided by blue b. The probability that a child of these parents will have the brown divided by brown genotype is . 25. c. The probability that the child will have blue eye color is . 75.
C .25 .75
4-4 Which word is associated with multiplication when computing probabilities? Choose the correct answer below. A. Disjoint B. Not C. And D. Or
C. And
4-3 Complete the following statement. Upper P left parenthesis Upper A or Upper B right parenthesis indicates _______. Choose the correct answer below. A. the probability that event A or event B does not occur in a single trial. B. the probability that event A occurs in one trial followed by event B in another trial. C. the probability that A and B both occur in the same trial. D. the probability that in a single trial, event A occurs, event B occurs, or they both occur.
D
4-3 Decide whether the following two events are disjoint. 1. Randomly selecting someone who is married 2. Randomly selecting someone who is a bachelor Are the two events disjoint? A. No, because the events can occur at the same time. B. No, because the events cannot occur at the same time. C. Yes, because the events can occur at the same time. D. Yes, because the events cannot occur at the same time.
D
4-3 Determine whether the two events are disjoint for a single trial. (Hint: Consider "disjoint" to be equivalent to "separate" or "not overlapping".) Randomly selecting a truck from the vehicle assembly line and getting one that is free of defects. Randomly selecting a truck from the vehicle assembly line and getting one with a dead battery. Choose the correct answer below. A. The events are not disjoint. They can occur at the same time. B. The events are disjoint. The first event is the complement of the second. C. The events are not disjoint. The first event is not the complement of the second. D. The events are disjoint. They cannot occur at the same time.
D
4-3 Determine whether the two events are disjoint for a single trial. (Hint: Consider "disjoint" to be equivalent to "separate" or "not overlapping".) Receiving a phone call from a volunteer survey subject who believes that the next president needs to be a Democrat. Receiving a phone call from a volunteer survey subject who is opposed to Roe versus Wade being overturned. A. The events are disjoint. They cannot occur at the same time. B. The events are not disjoint. The first event is not the complement of the second. C. The events are disjoint. The first event is the complement of the second. D. The events are not disjoint. They can occur at the same time.
D
4-3 Determine whether the two events are disjoint for a single trial. (Hint: Consider "disjoint" to be equivalent to "separate" or "not overlapping.") Randomly selecting someone who plays baseball. Randomly selecting someone taking a statistics course. A. The events are not disjoint. The first event is not the complement of the second. B. The events are disjoint. The first event is the complement of the second. C. The events are disjoint. They cannot occur at the same time. D. The events are not disjoint. They can occur at the same time.
D
4-6 In horse racing, a trifecta is a bet that the first three finishers in a race are selected, and they are selected in the correct order. Does a trifecta involve combinations or permutations? Explain. Choose the correct answer below. A. Because the order of the first three finishers does not make a difference, the trifecta involves combinations. B. Because the order of the first three finishers does not make a difference, the trifecta involves permutations. C. Because the order of the first three finishers does make a difference, the trifecta involves combinations. D. Because the order of the first three finishers does make a difference, the trifecta involves permutations.
D
4.2 Which of the following is NOT a principle of probability? Choose the correct answer below. A. The probability of any event is between 0 and 1 inclusive. B. The probability of an impossible event is 0. C. The probability of an event that is certain to occur is 1. D. All events are equally likely in any probability procedure.
D
4-4 For the given pair of events A and B, complete parts (a) and (b) below. A: When a baby is born, it is a girl. B: When a 16-sided die is rolled, the outcome is 10. a. Determine whether events A and B are independent or dependent. (If two events are technically dependent but can be treated as if they are independent according to the 5% guideline, consider them to be independent.) b. Find P(A and B), the probability that events A and B both occur. a. Choose the correct answer below. A. The two events are independent because the 5% guideline indicates that they may be treated as independent. B. The two events are dependent because the occurrence of one affects the probability of the occurrence of the other. C. The two events are dependent because the occurrence of one does not affect the probability of the occurrence of the other. D. The two events are independent because the occurrence of one does not affect the probability of the occurrence of the other. b. The probability that events A and B both occur is . 0313.
D .0313
4.2 Which of the following values cannot be probabilities? 0, negative 0.41, StartRoot 2 EndRoot, 5 divided by 3, 0.01, 1.21, 1, 3 divided by 5 Select all the values that cannot be probabilities. A. three fifths B. 0.01 C. 0 D. 1 E. negative 0.41 F. five thirds G. StartRoot 2 EndRoot H. 1.21
E F G H
4-5 Confusion of the inverse occurs when we incorrectly believe _______.
P(B|A)=P(A|B)
4-3 When using the _______ always be careful to avoid double-counting outcomes.
addition rule
4.2 If a couple were planning to have three children, the sample space summarizing the gender outcomes would be: bbb, bbg, bgb, bgg, gbb, gbg, ggb, ggg. a. Construct a similar sample space for the possible hair color outcomes (using b for brown dash haired and r for red dash headed) of two children. b. Assuming that the outcomes listed in part (a) were equally likely, find the probability of getting two red dash headed children. c. Find the probability of getting exactly one brown dash haired child and one red dash headed child. a. What is the sample space? bb comma br comma rr comma rb (Use a comma to separate answers as needed.) b. Find the probability of getting two red dash headed children . 25 (Type an exact answer.) c. Find the probability of getting one brown dash haired child and one red dash headed child. . 5 (Type an exact answer.)
bb, br, rr, rb .25 .5
4-3 A _______ is any event combining two or more simple events.
compound event
4-5 A _______ probability of an event is a probability obtained with knowledge that some other event has already occurred.
conditional
4-3 Events that are _______ cannot occur at the same time.
disjoint
4.2 The classical approach to probability requires that the outcomes are _______.
equally likely
4-4 Selections made with replacement are considered to be _______.
independent
4-4 Two events A and B are _______ if the occurrence of one does not affect the probability of the occurrence of the other.
independent
4-5 The complement of "at least one" is _______.
none
4-5 "At least one" is equivalent to _______.
one or more
4-6 If the order of the items selected matters, then we have a _______.
permutation problem
4-3 P (A right) plus P(A overbar) = 1 is one way to express the _______.
rule of complementary events
4.2 The _________ for a procedure consists of all possible simple events or all outcomes that cannot be broken down any further.
sample space
4-6 For a sequence of two events in which the first event can occur m ways and the second event can occur n ways, the events together can occur a total of (m)(n) ways. This is called _______.
the fundamental counting rule
4.2 As a procedure is repeated again and again, the relative frequency of an event tends to approach the actual probability. This is known as _______.
the law of large numbers
4-4 A picture of line segments branching out from one starting point illustrating the possible outcomes of a procedure is called a _______.
tree diagram
