Question

Suppose that the probability that Sally eats ice cream for dessert is p, and the probability that she eats cake is r = 1 – p. Let P_n be the probability that in n days, there are never two days in a row that Sally's had cake for desert.

a) Find P_2 and P_3 .

b) By conditioning on the outcome of the first day's dessert, find a recursive formula for P_n in terns of P_{n-1} and P_{n-2} .

c) Suppose that p = 0.3. Use the recursive formula to compute the probability of Sally eating cake at least two days in a row over the course of one week (7 days).

Answer 1