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 third student keeps buying chocolate bars until he finds 5 prize vouchers. Let W be the numbers of bars
before getting the 5 prize vouchers.

(i) Write down the pmf of W.

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