Problem #PRU-65276

Problems Probability and statistics Probability theory Discrete distribution Calculus Number sequences Limit of a sequence, convergence Number e

Problem

On the occasion of the beginning of the winter holidays all of the boys from class 8B went to the shooting range. It is known that there are \(n\) boys in 8B. There are \(n\) targets at the shooting range which the class attended. Each of the boys randomly chooses a target, while some of the boys could choose the same target. After this, all of the boys simultaneously attempt to shoot their target. It is known that each of the boys hits their target. The target is considered to be affected if at least one boy has hit it.

a) Find the average number of affected targets.

b) Can the average number of affected targets be less than \(n/2\)?