Chapter 17

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 \(\mathrm{AB}\) blood? b) What's the probability that there is a Type \(\mathrm{AB}\) donor among the first 5 people checked? c) What's the probability that the first Type \(\mathrm{AB}\) donor will be found among the first 6 people? d) What's the probability that we won't find a Type \(\mathrm{AB}\) donor before the 10 th person?

Assume that \(13 \%\) of people are left-handed. If we select 5 people at random, find the probability of each outcome described below. 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.

An Olympic archer is able to hit the bull's-eye \(80 \%\) of the time. Assume each shot is independent of the others. If she shoots 6 arrows, what's the probability of each of the following results? a) Her first bull's-eye comes on the third arrow. b) She misses the bull's-eye at least once. c) Her first bull's-eye comes on the fourth or fifth arrow. d) She gets exactly 4 bull's-eyes. e) She gets at least 4 bull's-eyes. f) She gets at most 4 bull's-eyes.

It is generally believed that nearsightedness affects about \(12 \%\) of all children. A school district tests the vision of 169 incoming kindergarten children. How many would you expect to be nearsighted? With what standard deviation?

At a certain college, \(6 \%\) of all students come from outside the United States. Incoming students there are assigned at random to freshman dorms, where students live in residential clusters of 40 freshmen sharing a common lounge area. How many international students would you expect to find in a typical cluster? With what standard deviation?

A certain tennis player makes a successful first serve \(70 \%\) of the time. Assume that each serve is independent of the others. If she serves 6 times, what's the probability she gets a) all 6 serves in? b) exactly 4 serves in? c) at least 4 serves in? d) no more than 4 serves in?

A wildlife biologist examines frogs for a genetic trait he suspects may be linked to sensitivity to industrial toxins in the environment. Previous research had established that this trait is usually found in 1 of every 8 frogs. He collects and examines a dozen frogs. If the frequency of the trait has not changed, what's the probability he finds the trait in a) none of the 12 frogs? b) at least 2 frogs? c) 3 or 4 frogs? d) no more than 4 frogs?

A lecture hall has 200 seats with folding arm tablets, 30 of which are designed for left-handers. The typical size of classes that meet there is 188, and we can assume that about \(13 \%\) of students are left-handed. What's the probability that a right-handed student in one of these classes is forced to use a lefty arm tablet?

An airline, believing that \(5 \%\) of passengers fail to show up for flights, overbooks (sells more tickets than there are seats). Suppose a plane will hold 265 passengers, and the airline sells 275 tickets. What's the probability the airline will not have enough seats, so someone gets bumped?