Question 1: (20 points)
Three men A, B, and C shoot at a target. Suppose that A shoots three times and the probability that he will hit the target on any given shot is \( 1 / 8, B \) shoots five times and the probability that he will hit the target on any given shot is \( 1 / 4 \), and \( C \) shoots twice and the probability that he will hit the target on any given shot is \( 1 / 2 \). Assume also that all shots at the target are independent.
a. What is probability that exact two targets are hit?
b. What is the expected number of times that the target will be hit?
c. What is the variance of the number of times that the target will be hit?