CH4 Stat
"At least one" is equivalent to _______.
"At least one" is equivalent to "one or more."
The classical approach to probability requires that the outcomes are _______
equally likely.
When a man observed a sobriety checkpoint conducted by a police department, he saw 652 drivers were screened and 4 were arrested for driving while intoxicated. Based on those results, we can estimate that Upper P left parenthesis Upper W right parenthesisequals0.00613, where W denotes the event of screening a driver and getting someone who is intoxicated. What does Upper P left parenthesis Upper W overbar right parenthesis denote, and what is its value?
. Upper P left parenthesis Upper W overbar right parenthesis denotes the probability of screening a driver and finding that he or she is not intoxicated. 1-.00913 =.99387
Which word is associated with multiplication when computing probabilities?
and
Find the probability that when a couple has two children, at least one of them is a boy. (Assume that boys and girls are equally likely.)
3/4
In an experiment, college students were given either four quarters or a $1 bill and they could either keep the money or spend it on gum. The results are summarized in the table. Complete parts (a) through (c) below. Purchased Gum Kept the Money Students Given Four Quarters 34 17 Students Given a $1 Bill 11 29
34+17=51 a. 34/51=.667 b.17/51=.334 c. A student given four quarters is more likely to have spent the money.
In a study of helicopter usage and patient survival, among the 55 comma 709 patients transported by helicopter, 261 of them left the treatment center against medical advice, and the other 55 comma 448 did not leave against medical advice. If 40 of the subjects transported by helicopter are randomly selected without replacement, what is the probability that none of them left the treatment center against medical advice?
55448/55709= .9953...^40
A _______ is any event combining two or more simple events.
A compound event is any event combining two or more simple events.
A _______ probability of an event is a probability obtained with knowledge that some other event has already occurred.
A conditional probability of an event is a probability obtained with knowledge that some other event has already occurred.
A picture of line segments branching out from one starting point illustrating the possible outcomes of a procedure is called a _______.
A picture of line segments branching out from one starting point illustrating the possible outcomes of a procedure is called a tree diagram.
Use the data in the following table, which lists drive-thru order accuracy at popular fast food chains. Assume that orders are randomly selected from those included in the table. The probability of getting an order from restaurant Upper A or Upper D or an order that is not accurate is
A+D+all ina / all
Which of the following is NOT a principle of probability?
All events are equally likely in any probability procedure.
As a procedure is repeated again and again, the relative frequency of an event tends to approach the actual probability. This is known as _______.
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.
Use the data in the following table, which lists drive-thru order accuracy at popular fast food chains. Assume that orders are randomly selected from those included in the table.
The probability of getting an order that is not accurate is add not accurate/add all 145/1135=.12775 =.128
If A denotes some event, what does Upper A overbar denote? If P(A)equals0.008, what is the value of P(Upper A overbar)?
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.
Events that are _______ cannot occur at the same time.
Events that are disjoint cannot occur at the same time.
In a computer instant messaging survey, respondents were asked to choose the most fun way to flirt, and it found that P(D)equals0.760, 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?
PD is the probability of randomly selecting someone who does not choose a direct in-person encounter as the most fun way to flirt. 1-.760 = .24
Fill in the blank. The _______ event A occurring are the ratio StartFraction Upper P left parenthesis Upper A right parenthesis Over Upper P left parenthesis Upper A overbar right parenthesis EndFraction .
The actual odds in favor of event A occurring are the ratio StartFraction Upper P left parenthesis Upper A right parenthesis Over Upper P left parenthesis Upper A overbar right parenthesis EndFraction .
The _______ for a procedure consists of all possible simple events or all outcomes that cannot be broken down any further.
The sample space for a procedure consists of all possible simple events or all outcomes that cannot be broken down any further.
The complement of "at least one" is _______.
The complement of "at least one" is "none."
Assume that 1800 births are randomly selected and 899 of the births are girls. Use subjective judgment to describe the number of girls as significantly high, significantly low, or neither significantly low nor significantly high.
The number of girls is neither significantly low nor significantly high.
Subjects for the next presidential election poll are contacted using telephone numbers in which the last four digits are randomly selected (with replacement). Find the probability that for one such phone number, the last four digits include at least one 0.
The probability is 0.344.
When randomly selecting adults, let M denote the event of randomly selecting a male and let B denote the event of randomly selecting someone with blue eyes. What does Upper P left parenthesis M|B right parenthesis represent? Is Upper P left parenthesis M|B right parenthesis the same as Upper P left parenthesis B|M right parenthesis?
The probability of getting a male, given that someone with blue eyes has been selected. No, because Upper P left parenthesis B|M right parenthesis represents the probability of getting someone with blue eyes, given that a male has been selected.
Let event Aequalssubject is telling the truth and event Bequalspolygraph test indicates that the subject is lying. Use your own words to translate the notation Upper P left parenthesis B|A right parenthesis into a verbal statement.
The probability that the polygraph indicates lying given that the subject is actually telling the truth.
Two events A and B are _______ if the occurrence of one does not affect the probability of the occurrence of the other.
Two events A and B are independent if the occurrence of one does not affect the probability of the occurrence of the other.
When randomly selecting an adult, A denotes the event of selecting someone with blue eyes. What do Upper P left parenthesis Upper A right parenthesis and Upper P left parenthesis Upper A overbar right parenthesis represent?
Upper P left parenthesis Upper A right parenthesis represents the probability of selecting an adult with blue eyes. Upper P left parenthesis Upper A overbar right parenthesis represents the probability of selecting an adult who does not have blue eyes.
When using the _______ always be careful to avoid double-counting outcomes.
When using the addition rule always be careful to avoid double-counting outcomes.
A modified roulette wheel has 28 slots. One slot is 0, another is 00, and the others are numbered 1 through 26, respectively. You are placing a bet that the outcome is an even number. (In roulette, 0 and 00 are neither odd nor even.)
a. 26/2=13 ans: 13/28 b. 1-13/28 15/28 / 13/28 15:13 c. When you bet that the outcome is an even number, the payoff odds are 1:1. How much profit do you make if you bet $19 and win? 19 d. How much profit should you make on the $19 bet if you could somehow convince the casino to change its payoff odds so that they are the same as the actual odds against winning? $19*(15/13) $21.92
n an experiment, college students were given either four quarters or a $1 bill and they could either keep the money or spend it on gum. The results are summarized in the table. Complete parts (a) through (c) below.
a. Find the probability of randomly selecting a student who spent the money, given that the student was given four quarters. The probability is 0.690. b. Find the probability of randomly selecting a student who spent the money, given that the student was given a $1 bill. The probability is 0.347. c. What do the preceding results suggest? A student given four quarters is more likely to have spent the money than a student given a $1 bill.
Refer to the figure below in which surge protectors p and q are used to protect an expensive high-definition television. If there is a surge in the voltage, the surge protector reduces it to a safe level. Assume that each surge protector has a 0.89 probability of working correctly when a voltage surge occurs. Complete parts (a) through (c) below.
a. If the two surge protectors are arranged in series, what is the probability that a voltage surge will not damage the television? 1-.89=.11 .11*.11=.0121 1-.0121=.9879 b. If the two surge protectors are arranged in parallel, what is the probability that a voltage surge will not damage the television? .89*.89=.7921 c. Which arrangement should be used for better protection? The series arrangment provides better protection because it has a higher probability of protection.
The conditional probability of B given A can be found by _______.
assuming that event A has occurred, and then calculating the probability that event B will occur
Use the following results from a test for marijuana use, which is provided by a certain drug testing company. Among 145 subjects with positive test results, there are 24 false positive results. Among 159 negative results, there are 5 false negative results. Complete parts (a) through (c). (Hint: Construct a table.)
table add ...
In a clinical trial of 2066 subjects treated with a certain drug, 24 reported headaches. In a control group of 1680 subjects given a placebo, 22 reported headaches. Denoting the proportion of headaches in the treatment group by pt and denoting the proportion of headaches in the control (placebo) group by pc, the relative risk is pt/pc. The relative risk is a measure of the strength of the effect of the drug treatment. Another such measure is the odds ratio, which is the ratio of the odds in favor of a headache for the treatment group to the odds in favor of a headache for the control (placebo) group, found by evaluating StartFraction p Subscript t Baseline divided by left parenthesis 1 minus p Subscript t Baseline right parenthesis Over p Subscript c Baseline divided by left parenthesis 1 minus p Subscript c Baseline right parenthesis EndFraction . The relative risk and odds ratios are commonly used in medicine and epidemiological studies. Find the relative risk and odds ratio for the headache data. What do the results suggest about the risk of a headache from the drug treatment?
(24/2066)/(22/1680) The relative risk =.887 (24/2066)/(1-(24-2066)) / (22/1680)/(1-(22/1680)) The odds ratio=. 886 The drug does not appear to pose a risk of headaches because p Subscript t is slightly less than p Subscript c.
A research center poll showed that 77% 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?
1-.77 =.23
Confusion of the inverse occurs when we incorrectly believe _______.
P(BIA)= P(AIB)
Use the data in the following table, which lists drive-thru order accuracy at popular fast food chains. Assume that orders are randomly selected from those included in the table. Drive-thru Restaurant A B C D Order Accurate 315 275 238 140 Order Not Accurate 39 59 40 17
The probability of getting food that is not from Restaurant A is add resturant letter (A/B/C) / add all order 354/1123=.315227 1-.315227= .685
A study of 420,095 cell phone users resulted in 135 who developed cancer of the brain or nervous system. When comparing this sample group to another group of people who did not use cell phones, it was found that there is a probability of 0.512 of getting such sample results by chance. What do you conclude?
The probability shows that the sample results could have easily occurred by chance. It appears that there is not sufficient evidence to conclude that cell phones have an effect on cancer of the brain or nervous system.
Selections made with replacement are considered to be _______.
Selections made with replacement are considered to be independent.
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 45 13 Subject Is Not a Drug User 19 37
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.
Assuming boys and girls are equally likely, find the probability of a couple having a baby girl when their sixth child is born, given that the first five children were all girls.
The probability is one half .1/2
What does P(B|A) represent?
The probability of event B occurring after it is assumed that event A has already occurred
There are 15,958,866 adults in a region. If a polling organization randomly selects 1235 adults without replacement, are the selections independent or dependent? If the selections are dependent, can they be treated as independent for the purposes of calculations?
The selections are dependent, because the selection is done without replacement. Yes, because the sample size is less than 5% of the population.
A study on the enhancing effect of coffee on long-term memory found that 35 participants given 200 mg of caffeine performed better on a memory test 24 hours later compared to the placebo group that received no caffeine. a. There was a probability of 0.049 that the difference between the coffee group and the placebo group was due to chance. What do you conclude? b. A group given a higher dose of 300 mg performed better than the 200 mg group, with a probability of 0.75 that this difference is due to chance. What do you conclude?
a. The probability shows that the sample results could not have easily occurred by chance. It appears that there is sufficient evidence to conclude that 200 mg of caffeine does have an effect on memory. b. The probability shows that the sample results could have easily occurred by chance. It appears that there is not sufficient evidence to conclude that the effects from the 300 mg treatment and the 200 mg treatment are different.
Use the following results from a test for marijuana use, which is provided by a certain drug testing company. Among 140 subjects with positive test results, there are 24 false positive results; among 160 negative results, there are 2 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.)
add and divide all
Use the data in the following table, which lists drive-thru order accuracy at popular fast food chains. Assume that orders are randomly selected from those included in the table. The probability of getting an order from Restaurant C or an order that is not accurate is
all inacurate + C accurate / ALL =.345 Are the events of selecting an order from Restaurant C and selecting an inaccurate order disjoint events? The events are not disjoint because it is possible to receive an inaccurate order from Restaurant C.
In a certain country, the true probability of a baby being a girl is 0.486. Among the next four randomly selected births in the country, what is the probability that at least one of them is a boy?
1-(.486^4) 4random
Testing for a disease can be made more efficient by combining samples. If the samples from three people are combined and the mixture tests negative, then all three samples are negative. On the other hand, one positive sample will always test positive, no matter how many negative samples it is mixed with. Assuming the probability of a single sample testing positive is 0.05, find the probability of a positive result for three samples combined into one mixture. Is the probability low enough so that further testing of the individual samples is rarely necessary?
1-.05=.95 1-(.95^3) =.143 Is the probability low enough so that further testing of the individual samples is rarely necessary? The probability is not low, so further testing of the individual samples will not be a rarely necessary event.
On their first date, Kelly asks Mike to guess the date of her birth, not including the year. Complete parts a through c below.
1/365 Yes, it is unlikely for Mike to guess correctly on his first try, as the probability of a correct guess is very low. Mike already knew, as the probability of a correct guess is very low.
In an experiment, college students were given either four quarters or a $1 bill and they could either keep the money or spend it on gum. The results are summarized in the table. Complete parts (a) through (c) below. Purchased Gum Kept the Money Students Given Four Quarters 26 16 Students Given a $1 Bill 17 29
17+29=46 a. 17/46=.37 b.29/46=.630 c. A student given a $1 bill is more likely to have kept the money.
A weather forecasting website indicated that there was a 45% chance of rain in a certain region. Based on that report, which of the following is the most reasonable interpretation?
There is a 0.45 probability that it will rain somewhere in the region at some point during the day.
Assume that there is a 11% rate of disk drive failure in a year. a. If all your computer data is stored on a hard disk drive with a copy stored on a second hard disk drive, what is the probability that during a year, you can avoid catastrophe with at least one working drive? b. If copies of all your computer data are stored on four independent hard disk drives, what is the probability that during a year, you can avoid catastrophe with at least one working drive?
a. 1-(.11^2) =.9879 b. 1-(.11^4) four b/cit says four
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.
add the possitives and divide the Q 17+42=.712
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 did not have the disease.
just the No's: 5+144=149 144/149=.966
Complete the following statement. Upper P left parenthesis Upper A or Upper B right parenthesis indicates _______.
the probability that in a single trial, event A occurs, event B occurs, or they both occur.
When randomly selecting an adult, let B represent the event of randomly selecting someone with type B blood. Write a sentence describing what the rule of complements below is telling us. Upper P left parenthesis Upper B or Upper B overbar right parenthesisequals1
It is certain that the selected adult has type B blood or does not have type B blood.
The accompanying table shows the results from a test for a certain disease. Find the probability of selecting a subject with a negative test result, given that the subject has the disease. What would be an unfavorable consequence of this error?
Just the Yes's: 350+10=360 10/360=.028 The subject would not receive treatment and could spread the disease.
Fill in the blank. Upper P left parenthesis Upper A right parenthesisplusUpper P left parenthesis Upper A overbar right parenthesis = 1 is one way to express the _______.
plusUpper P left parenthesis Upper A overbar right parenthesis = 1 is one way to express the rule of complementary events.
Use the data in the following table, which lists drive-thru order accuracy at popular fast food chains. Assume that orders are randomly selected from those included in the table. If two orders are selected, find the probability that they are both from Restaurant D. a. Assume that the selections are made with replacement. Are the events independent? b. Assume that the selections are made without replacement. Are the events independent?
same but ^2nd power a. Assume that the selections are made with replacement. Are the events independent? The probability of getting two orders from Restaurant D is 0.0211. The events are independent because choosing the first order does not affect the choice of the second order. b. Assume that the selections are made without replacement. Are the events independent? The probability of getting two orders from Restaurant D is 0.0210. The events are not independent because choosing the first order affects the choice of the second order.
Use the data in the following table, which lists drive-thru order accuracy at popular fast food chains. Assume that orders are randomly selected from those included in the table. If two orders are selected, find the probability that they are both accurate. Complete parts (a) and (b) below.
to the ^2 again a. Assume that the selections are made with replacement. Are the events independent? The probability is 0.762. The events are independent. b. Assume that the selections are made without replacement. Are the events independent? The probability is 0.762. The events are not independent.
Among 6410 cases of heart pacemaker malfunctions, 355 were found to be caused by firmware, which is software programmed into the device. If the firmware is tested in 3 different pacemakers randomly selected from this batch of 6410 and the entire batch is accepted if there are no failures, what is the probability that the firmware in the entire batch will be accepted? Is this procedure likely to result in the entire batch being accepted?
(1- 355/6410)^3 The probability is . 843. This procedure is likely to result in the entire batch being accepted.
Men have XY (or YX) chromosomes and women have XX chromosomes. X-linked recessive genetic diseases (such as juvenile retinoschisis) occur when there is a defective X chromosome that occurs without a paired X chromosome that is not defective. Represent a defective X chromosome with lowercase x, so a child with the xY or Yx pair of chromosomes will have the disease and a child with XX or XY or YX or xX or Xx will not have the disease. Each parent contributes one of the chromosomes to the child. Complete parts a through d below.
. If a father has the defective x chromosome and the mother has good XX chromosomes, what is the probability that a son will inherit the disease? 0 b. If a father has the defective x chromosome and the mother has good XX chromosomes, what is the probability that a daughter will inherit the disease? 0 c. If a mother has one defective x chromosome and one good X chromosome and the father has good XY chromosomes, what is the probability that a son will inherit the disease? . 5 d. If a mother has one defective x chromosome and one good X chromosome and the father has good XY chromosomes, what is the probability that a daughter will inherit the disease? 0
he principle of redundancy is used when system reliability is improved through redundant or backup components. Assume that a student's alarm clock has a 19.2% daily failure rate. Complete parts (a) through (d) below.
.192 .192*.192=.036 .192*.192*.192=.00708 Yes, because total malfunction would not be impossible, but it would be unlikely.
Hospitals typically require backup generators to provide electricity in the event of a power outage. Assume that emergency backup generators fail 22% of the times when they are needed. A hospital has two backup generators so that power is available if one of them fails during a power outage. Complete parts (a) and (b) below.
.22*.22=.0484 1-.0484=.9516 1-.95 No, because both generators fail about 5% of the time they are needed. Given the importance of the hospital's needs, the reliability should be improved.
Based on a poll, 69% of Internet users are more careful about personal information when using a public Wi-Fi hotspot. What is the probability that among three randomly selected Internet users, at least one is more careful about personal information when using a public Wi-Fi hotspot? How is the result affected by the additional information that the survey subjects volunteered to respond?
1-((1-.69)^3) It is very possible that the result is not valid because the sample may not be representative of the people who use public Wi-Fi.
Find the indicated complement. A certain group of women has a 0.79% rate of red/green color blindness. If a woman is randomly selected, what is the probability that she does not have red/green color blindness?
1-.0079 = .9921
To reduce laboratory costs, water samples from six public swimming pools are combined for one test for the presence of bacteria. Further testing is done only if the combined sample tests positive. Based on past results, there is a 0.009 probability of finding bacteria in a public swimming area. Find the probability that a combined sample from six public swimming areas will reveal the presence of bacteria. Is the probability low enough so that further testing of the individual samples is rarely necessary?
1-.009=.991 1-(.991^6) 6pools =.053 The probability is quite low, indicating that further testing of the individual samples will be a rarely necessary event.
Use the data in the following table, which lists drive-thru order accuracy at popular fast food chains. Assume that orders are randomly selected from those included in the table. The probability of getting an order from Restaurant A or an order that is accurate is
all accurate + A inaccurate / ALL .8... The events are not disjoint because it is possible to receive an accurate order from Restaurant A.
he sample space listing the eight simple events that are possible when a couple has three children is {bbb, bbg, bgb, bgg, gbb, gbg, ggb, ggg}. After identifying the sample space for a couple having four children, find the probability of getting one girl and three boys left parenthesis in any order right parenthesis. Identify the sample space for a couple having four children.
bggg gbgg ggbg gggb bbgg bgbg bggb gbbg gbgb ggbb bbbg bbgb bgbb gbbb {gggg, bggg, gbgg, ggbg, gggb, bbgg, bgbg, bggb, gbbg, gbgb, ggbb, bbbg, bbgb, bgbb, gbbb, bbbb}
