(a) Note: In a one card pack, the probability of a particular card is 1/4. In a two card pack the probability of a particular card is 2/4.
So the total probability of getting a particular card is (1/5)(2/4) + (4/5)(1/4) = 6/20 = 3/10.
So now it's a binomial distribution problem ...... X is the random variable number of students who get the card they need (and hence complete their set), n = 20, p = 3/10.
E(X) = np = .....