An archer is able to hit the bull's eye 65% of the time.If she keeps shooting arrows until she hits the bull's-eye,how long do you expect it will take? Assume each shot is independent of the others.
A)2.86 shots
B)0.35 shots
C)1.54 shots
D)0.65 shots
E)65 shots

Question

Quizplus · Accepted Answer

We can model this situation as a geometric distribution with p=0.65, where X is the number of shots until the first success (i.e. hitting the bull's-eye). The expected value of a geometric distribution is 1/p, so in this case, E(X) = 1/0.65 = 1.54. Therefore, the archer is expected to shoot 1.54 times before hitting the bull's-eye.

An Archer Is Able to Hit the Bull's Eye 65