Probability - CH 4
Determine the written description of the complement of the given event. "When six digital pianos are shipped, at least one of them isis defective."
All of them are free of defects
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.
P(subject had a positive test result or a negative test result) = 1
The data in the following table summarize results from 153 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.
The probability is 0.187494 No, not unlikely because its probability is greater than 0.05
Is this probability high enough to ensure flight safety?
Yes, the probability is high enough to ensure flight safety because it is close to 1.
Which of the following values cannot be probabilities? 0, 1.31, 3/5, −0.52, 0.04, 5/3, 1, √2
All the values that cannot be probabilities are: √2, 1.31, 5/3, -0.52
A fan of country music plans to make a custom CD with 14 of her 28 favorite songs. How many different combinations of 14 songs are possible? Is it practical to make a different CD for each possible combination?
How many different combinations of 14 songs are possible? 40116600 No, it is not practical to make a different CD for each possible combination because the number of possible combinations is very large.
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 16−18 age bracket? Consider an event to be "unlikely" if its probability is less than or equal to 0.05.
No, not unlikely Yes, its high enough
Decide whether the following two events are disjoint. 1. Randomly selecting someone who owns a car 2. Randomly selecting a married male
No, because the events can occur at the same time.
The following data summarizes results from 1037 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.
P(pedestrian was intoxicated or driver was intoxicated) = 0.429
A presidential candidate plans to begin her campaign by visiting the capitals in 3 of 46 states. What is the probability that she selects the route of three 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 three specific capitals) = 1 / 91080 No, it is not practical to list all of the different possible routes because the number of possible permutations is very large.
Why does the usual rounding rule of three significant digits not work here?
Rounding the result to three significant digits yields 1.00, which is misleading because it suggests that it is certain that both radios will work correctly.
Determine whether the two events are disjoint for a single trial. (Hint: Consider "disjoint" to be equivalent to "separate" or "not overlapping".) 1"Receiving a phone call from a volunteer survey subject who believes that the next president needs to be a Republican" 2"Receiving a phone call from a volunteer survey subject who is opposed to the Roe versus Wade decision."
The events are not disjoint. They can occur at the same time.
A classic counting problem is to determine the number of different ways that the letters of "incidentally" can be arranged. Find that number.
The number of different ways that the letters of "incidentally" can be arranged is 59875200.
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
When testing for current in a cable with eleven color-coded wires, the author used a meter to test four wires at a time. How many different tests are required for every possible pairing of four wires?
The number of tests required is 330.
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. No. The second event involves more possible outcomes.
If a couple plans to have 5 children, what is the probability that there will be at least one boy? 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 boy in 5 children?
The probability is 31/32. Yes because the probability is close to 1.
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?
The probability of a false positive test result is 0.17 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.
In a genetics experiment on peas, one sample of offspring contained 369 green peas and 460 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 3/4 that was expected?
The probability of getting a green pea is approximately 0.445 No, it is not reasonably close.
Winning the jackpot in a particular lottery requires that you select the correct three numbers between 1 and 26 and, in a separate drawing, you must also select the correct single number between 1 and 47. Find the probability of winning the jackpot.
The probability of winning the jackpot is 1/122200
In a test of a gender-selection technique, results consisted of 219 baby girls and 11 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 0.952. Yes, its effective
Among 500 randomly selected drivers in 16−18 age bracket, 443 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?
The probability that a randomly selected person in the 16−18 age bracket will be in a car crash this year is approximately 0.886
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 0.439 for a negative test result?
The probability that a randomly selected polygraph test subject was not lying is 0.467. 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.
Use the following results from a test for marijuana use, which is provided by a certain drug testing company. Among 146 subjects with positive test results, there are 24 false positive results; among 151 negative results, there are 4 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.
The probability that a randomly selected subject tested negative or did not use marijuana is 0.589
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? 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.
The probability that all four test subjects had a true negative test result when they are randomly selected with replacement is 0.076 No, not unlikely because the probability of the event is greater than 0.05. The probability that all four test subjects had a true negative test result when they are randomly selected without replacement is 0.072 No, not unlikely because the probability of the event is greater than 0.05.
Commercial aircraft used for flying in instrument conditions are required to have two independent radios instead of one. Assume that for a typical flight, the probability of a radio failure is 0.0035. What is the probability that a particular flight will be safe with at least one working radio?
The probability that at least one of the radios works correctly is 0.999988. {formula: p*p = p^2, so 1-p^2= answer}
The probability of a randomly selected car crashing during a year in a certain country is 0.0459. 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 0.1315. Yes, the three cars are not randomly selected.
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 0.17
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 2000 CDs, and 611 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?
The probability that the whole batch is accepted is 0.335 No, because only a probability of 1 would indicate the entire batch consists of good CDs.
Refer to the table below. Given that 2 of the 147 subjects are randomly selected, complete parts (a) and (b). a. Assume that the selections are made with replacement. What is the probability that the 2 selected subjects are both group A and type Rh+? b. Assume the selections are made without replacement. What is the probability that the 2 selected subjects are both group A and type Rh+?
a. 0.0816 b. 0.0802
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 0 boys. b. Among three children, there is exactly 1 boy. c. Among three children, there are exactly 3 girls.
a. 1/8 b. 3/8 c. 1/8
In designing an experiment involving a treatment applied to 6 test subjects, researchers plan to use a simple random sample of 6 subjects selected from a pool of 28 available subjects. (Recall that with a simple random sample, all samples of the same size have the same chance of being selected.) Answer the questions below. a. How many different simple random samples are possible? b. What is the probability of each simple random sample in this case?
a. 376740 b. 1/376740
In a market research survey of 2869 motorists, 291 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? b. If 50 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?
a. The probability is 0.8986 b. The probability is 0.0048. The 5% guideline should be applied in this case.
A test for marijuana usage was tried on 217 subjects who did not use marijuana. The test result was wrong 69 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 .318 b. No, not unlikely (greater than 0.05)
For the given pair of events A and B, complete parts (a) and (b) below. EVENT A: When a page is randomly selected and ripped from a 2222-page document and destroyed, it is page 55. EVENT B: When a different page is randomly selected and ripped from the document, it is page 99. 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. 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 0.0022.
Consider a bag that contains 226 coins of which 4 are rare Indian pennies. For the given pair of events A and B, complete parts (a) and (b) below. EVENT A: When one of the 226 coins is randomly selected, it is one of the 4 Indian pennies. EVENT B: When another one of the 226 coins is randomly selected (with replacement), it is also one of the 4 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. 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 0.000313
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 five different members. There are 13 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? b. How many different ways can the committee be appointed? c. What is the probability of randomly selecting the committee members and getting the five youngest of the qualified candidates?
a. There are 17,160 different ways to appoint the officers. b. There are 1287 different ways to appoint the committee. c. P(getting the five youngest of the qualified candidates) = 1/1287
Pollsters are concerned about declining levels of cooperation among persons contacted in surveys. A pollster contacts 96 people in the 18-21 age bracket and finds that 67 of them respond and 29 refuse to respond. When 252 people in the 22-29 age bracket are contacted, 213 respond and 39 refuse to respond. Suppose that one of the 348 people is randomly selected. Find the probability of getting someone in the 22-29 age bracket or someone who responded.
P(person is in the 22-29 age bracket or responded) = 0.917
The following data lists the number of correct and wrong dosage amounts calculated by 28 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 14 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?
P(physician calculated the dose correctly) = 0.429 No. One would want this probability to be very high.
The table below displays results from experiments with polygraph instruments. Find P(subject lied | negative test result). Compare this result with the probability of selecting a subject with a negative test result, given that the subject lied. Are P(subject lied | negative test result) and P(negative test result | subject lied) equal?
P(subject lied | negative test result) = 0.244 P(negative test result | subject lied) = 0.196 No, not equal
