Question: New bow. Our archer in Exercise 18 purchases a new bow, hoping that it will improve her success rate to more than 80% bull's-eyes. She is delighted when she first tests her new bow and hits 6 consecutive bull's-eyes. Do you think this is compelling evidence that the new bow is better? In other words, is a streak like this unusual for her? Explain.
Exercise: 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.