A group of 2n people, consisting of n men and n women, are to be independently distributed among m rooms Each woman chooses room j with probability p, while each man chooses it with probability q,, j 1,.., m Let X denote the number of rooms that will contain exactly one man and one woman.. =

(a) Find E[X].

(b) Bound P{|X | > b} for b > 0. =