Fillable Problems Probability Models Worksheets (Page 2 of 11) in pdf

7. Hoops. 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.

8. Chips. 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?

9. More hoops. For the basketball player in Exercise 7, what's the expected number of shots until he misses?

10. Chips ahoy. For the computer chips described in Exercise 8, how many do you expect to test before finding a bad

one?

11. Blood. 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?

d) What's the probability that we won't find a Type AB donor before the 10th person?

12. Colorblindness. About 8% of males are colorblind. A researcher needs some colorblind 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 colorblind?

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 colorblind man found will be the sixth person checked?

d) What's the probability that she finds someone who is colorblind before checking the lOth man?

13. Lefties. 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 3lefties in the group.

f) There are no more than 3 lefties in the group.

14. Arrows. 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 result described below.

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.

15. Lefties redux. Consider our group of 5 people from Exercise 13.

a) How many lefties do you expect?

b) With what standard deviation?

c) If we keep picking people until we find a lefty, how long do you expect it will take?

16. More arrows. Consider our archer from Exercise 14.

a) How many bull's-eyes do you expect her to get?

b) With what standard deviation?

c) If she keeps shooting arrows until she hits the bull's eye, how long do you expect it will take?

Problems Probability Models Worksheets Page 2

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