Question: New bow, again. The archer in Exercise I continues shooting arrows, ending up with 45 bull's-eyes in 50 shots. Now are you convinced that the new bow is better? Explain.

Exercise I: New bow. Our archer in Exercise II 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 II: 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.