91Ó°ÊÓ

A Department of Transportation report about air travel found that airlines misplace about 5 bags per 1000 passengers. Suppose you are traveling with a group of people who have checked 22 pieces of luggage on your flight. Can you consider the fate of these bags to be Bernoulli trials? Explain.

A basketball player has made \(80 \%\) of his foul shots during the season. Assuming the shots are independent, find the probability that in tonight's game he a. misses for the first time on his fifth attempt. b. makes his first basket on his fourth shot. c. makes his first basket on one of his first 3 shots.

Suppose a computer chip manufacturer rejects \(2 \%\) of the chips produced because they fail presale testing. a. What's the probability that the fifth chip you test is the first bad one you find? b. What's the probability you find a bad one within the first 10 you examine?

Raaj works at the customer service call center of a major credit card bank. Cardholders call for a variety of reasons, but regardless of their reason for calling, if they hold a platinum card, Raaj is instructed to offer them a double-miles promotion. About \(10 \%\) of all cardholders hold platinum cards, and about \(50 \%\) of those will take the double-miles promotion. On average, how many calls will Raaj have to take before finding the first cardholder to take the double-miles promotion?

Justine works for an organization committed to raising money for Alzheimer's research. From past experience, the organization knows that about \(20 \%\) of all potential donors will agree to give something if contacted by phone. They also know that of all people donating, about \(5 \%\) will give \(\$ 100\) or more. On average, how many potential donors will she have to contact until she gets her first \(\$ 100\) donor?

Only \(4 \%\) of people have Type AB blood. a. On average, how many donors must be checked to find someone with Type AB blood? b. What's the probability that there is a Type AB donor among the first 5 people checked? c. What's the probability that the first Type AB donor will be found among the first 6 people?

About \(8 \%\) of males are color-blind. A researcher needs some color-blind subjects for an experiment and begins checking potential subjects. a. On average, how many men should the researcher expect to check to find one who is color-blind? b. What's the probability that she won't find anyone colorblind among the first 4 men she checks? c. What's the probability that the first color-blind man found will be the sixth person checked? d. What's the probability that she finds someone who is color-blind before checking the 10th man?

If you flip a fair coin 100 times, a. Intuitively, how many heads do you expect? b. Use the formula for expected value to verify your intuition.

An American roulette wheel has 38 slots, of which 18 are red, 18 are black, and 2 are green \((0\) and 00\()\). If you spin the wheel 38 times, a. Intuitively, how many times would you expect the ball to wind up in a green slot? b. Use the formula for expected value to verify your intuition.

Assume that \(13 \%\) of people are left-handed. If we select 5 people at random, find the probability of each outcome. a. The first lefty is the fifth person chosen. b. There are some lefties among the 5 people. C. The first lefty is the second or third person. d. There are exactly 3 lefties in the group. e. There are at least 3 lefties in the group. f. There are no more than 3 lefties in the group.