A type of chocolate bar does contain a prize voucher with probability p, 0 ≤ p ≤ 1. Whether or not a bar does contain a prize voucher is independent of other bars. A hungry student buys 8 chocolate bars. Let
X denote the number of bars without prize vouchers that she finds and its probability mass function (pmf) is given below:

A second student keeps buying chocolate bars until he finds a prize voucher. Let Y denote the number of
bars he buys before getting a bar with a prize voucher.

(i) What down the probability mass function of Y and verify whether it is pmf or not.

X:x 1 3 4 6 7 8 Pr(X:x) k4 ka k2 k1 k k, k2 k3 k4