Question

An Olympic archer can hit the bullseye 89% of the time. Assuming each shot is independent,

a) find the probability the first bullseye is on her third shot.

b) find the probability she has to shot at least 3 times prior to the first bullseye.

c) compute E(X), V(X), and ?.

Answer 1

a) probability the first bullseye is on her third shot =P(X=3)=P(first two shots are failure and 3rd shot is success)

=(1-0.89)²*0.89=0.0108

b)P( she has to shot at least 3 times prior to the first bullseye )=P(first 2 shots are failure)=(1-0.89)² =0.0121

c)

E(X)=1/p=1/0.89=1.1236

V(X)=(1-p)/p² =(1-0.89)/0.89² =0.1389

? =sqrt(0.1389)=0.3727