More arrows. Consider our archer from Exercise 20.
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?
Exercise 20
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 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.