Stats Ch. 12

Suppose that 34​% of people have a dog​, 15​% of people have a cat​, and 6​% of people own both. What is the probability that someone owns a dog or a cat​?

The probability of a person having a dog or a cat is .34-.06=.28 .15-.06=.09 .34+.15-.06=.43

A certain bowler can bowl a strike 70 % of the time. What is the probability that she

The probability of going three consecutive frames without a strike is 1-(.7)=.3 (.3)^3=.027 The probability of making her first strike in the third frame is (.3)(.3)(.7)=.063 The probability of having at least one strike in the first three frames is nothing 1-.027=.973 The probability of bowling a perfect game is nothing (.7)^12=.014

Insurance companies collect annual payments from drivers in exchange for paying for the cost of accidents. ​a) Why should someone be reluctant to accept a​ $1500 payment from a neighbor to cover that​ neighbor's automobile accidents in the next​ year? b) Why can the insurance company make that​ offer?

There is some chance the first person would have to pay out much more than the​ $1500. Many customers pay for insurance. The small risk for any one customer is spread among all.

Every​ morning, my neighbor goes out walking. I observe that​ 20% of the time she walks with her​ beagle, 70% of the time she walks with her golden​ retriever, and​ 30% of the time she walks alone. If these events are all​ disjoint, is this an example of a valid probability​ distribution?

This is nota valid probability distribution.

The prerequisite for a required course is that students must have taken either course A or course B. By the time they are​ juniors, 51​% of the students have taken course​ A, 21 % have had course​ B, and 6​% have done both.

a) What percent of the juniors are ineligible for the​ course? .51+.21-.06=.3 1-.3=.7

Police report that​ 78% of drivers are given a breath​ test, 36% a blood​ test, and​ 22% both tests. Find Upper P (breath test|blood test).

.22/.36

You wake up from a nightmare in which​ you've completely forgotten about the final exam in your stats class. Since you​ haven't studied, you estimate that there is an​ 80% chance of answering any individual problem correctly. The test is 5 questions long. If you wanted to find the probability you answer all the questions​ incorrectly, what could you​ do?

0.2 times 0.2 times 0.2 times 0.2 times 0.2

Our survey found that​ 56% of college students live on​ campus, 62% have a campus meal ​program, and​ 42% do both. In this​ example, what would be the denominator of the fraction if we wanted to find Upper P left parenthesis meal plan|live on campus right parenthesis​?

0.56

Suppose that 59​% of families living in a certain country own an HDTV and 28​% own a laptop. The Addition Rule might​ suggest, then, that 87​% of families own either an HDTV or a laptop. ​What's wrong with that​ reasoning?

A family may own both an HDTV and a laptop. The events are not​ disjoint, so the Addition Rule does not apply.

Every​ morning, my neighbor goes out walking. I observe that​ 20% of the time she walks with her​ beagle, 70% of the time she walks with her golden​ retriever, and​ 30% of the time she walks alone. Can the two events StartSet walk with beagle EndSet and StartSet walk with golden retriever EndSet be​ disjoint?

No

Dan's Diner employs three dishwashers. Al washes 40 % of the dishes and breaks only 1 % of those he handles. Betty and Chuck each wash 30 % of the​ dishes, and Betty breaks only 1 % of​ hers, but Chuck breaks 5 % of the dishes he washes. You go to​ Dan's for supper one night and hear a dish break at the sink.​ What's the probability that Chuck is on the​ job?

The probability that Chuck is on the job is .4*.01=.004 .4*.98=.392 .3*.01=.003 .3*.98=.294 .3*.05=.015 .3*.94=.282 .004+.003+.015=.022 .015/.022=.682

A consumer organization estimates that over a​ 1-year period 17​% of cars will need to be repaired​ once, 7​% will need repairs​ twice, and 2​% will require three or more repairs. What is the probability that a car chosen at random will need

The probability that a car will require no repairs is nothing .17+.07+.02=.26 1-.26=.74 The probability that a car will require no more than one repair is .74+.17=.91 The probability that a car will require some repairs is .17+.07+.02=.26

You purchased a​ five-pack of new light bulbs that were recalled because 12​% of the lights did not work. What is the probability that at least one of your lights is​ defective?

The probability that at least one of the light bulbs is defective is 1-.12=.88 (.88)^5=.528

A recent study conducted by a health statistics center found that 23​% of households in a certain country had no landline service. This raises concerns about the accuracy of certain​ surveys, as they depend on​ random-digit dialing to households via landlines. Pick four households from this country at random.

a) What is the probability that all four of them have a​ landline? 1-.23=.77 (.77)^4=.352 b)What is the probability that at least one of them does not have a​ landline? 1-.352=.648 c)What is the probability that at least one of them does have a​ landline? (.23)^4=.003 1-.003=.997

For each of the​ following, list the sample space and tell whether you think the outcomes are equally likely.

a)Which of the following is the sample space for recording the order of heads and tails when tossing 2 ​coins? Let H represent getting a head and T getting a tail. ​{HH, HT,​ TH, TT} Are the outcomes equally​ likely? Yes b) Which of the following is the sample space for the number of boys in the​ family? ​{0,1, 2​} Are the outcomes equally​ likely? No ​ c) What is the sample space for flipping a coin until you get a head or 4 consecutive tails? ​{H, TH, TTH, TTTH, TTTT​} Are the outcomes equally​ likely? No ​d) What is the sample space for the larger number when two dice are​ rolled? ​{1, 2,​ 3, 4,​ 5, 6} Are the outcomes equally​ likely? No

A display that helps us think through calculations with conditional probabilities and the general multiplication rule is a

tree diagram

In a large introductory statistics lecture​ hall, the professor reports that 55​% of the students enrolled have never taken a calculus​ course, 30​% have taken only one semester of​ calculus, and the rest have taken two or more semesters of calculus. The professor randomly assigns students to groups of three to work on a project for the course. You are assigned to be part of a group. What is the probability that of your other two​ groupmates,

​a) The probability that neither of your other two groupmates has studied calculus is .55*.55=.3025 b) The probability that both of your other two groupmates have studied at least one semester of calculus is 1-.55=.45 .45*.45=.2025 c) The probability that at least one of your other two groupmates has had more than one semester of calculus is .55+.30=.85 1-(.85)(.85)=.2775

A magazine published the results of an extensive investigation of broiler chickens purchased from food stores in 23 regions. Tests for bacteria in the meat showed that 58​% of the chickens were contaminated with​ campylobacter, 16​% with​ salmonella, and 8​% with both.

​a) What's the probability that a tested chicken was not contaminated with either kind of​ bacteria? .58+.16-.08=.66 1-.66=.34 b) Are the events​ disjoint? ​No, because there are outcomes that are common between them. c) Are the events​ independent? ​No, because the outcome of one influences the probability of the other.