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

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