10 hunters shoot at 10 ducks each choosing his target unifor

10 hunters shoot at 10 ducks each choosing his target uniformly at random. Each hunter hits his target with probability .6 independent of others. Let X be the number of ducks that escape. Find EX. (Hint: Let Xi = 1 if i-th duck escapes. What is the probability that hunter j hits duck i?)

Solution

Ex = 10 * 0.4 = 4

the mean number of ducks that escape is 4