50. There are three coins in a barrel. These coins, when flipped, will come up heads with respective probabilities 0.3, 0.5, 0.7. A coin is randomly selected from among these three and is then flipped ten times. Let N be the number of heads obtained on the ten flips.

(a) Find P{N = 0}.

(b) Find P{N = n}, n = 0, 1, . . . , 10.

(c) Does N have a binomial distribution?

(d) If you win $1 each time a head appears and you lose $1 each time a tail appears, is this a fair game? Explain.