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:

(i) What sort of distribution does X have? Write down its pmf form.
(ii) Draw the above pmf where 0 ≤ k > k1 > k2 > k3 > k4 ≤ 1.
(iii) How likely is it that the she finds seven or more bar without prize voucher?
(iv) What is the most likely numbers of vouchers that she finds?

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