Question

A door-to-door salesman expects to make a sale 24% of the time when starting the day. But making a sale increases his enthusiasm so much that the probability of a sale to the next customer is 0.52. If he makes no sale, the probability for a sale to the next customer stays at 0.24. What is the probability that he will make at least two sales with his first three visits?

Answer 1

P(atleast 2 sales) = P(2 sales) + P(3 sales)

P(3 sales) = 0.24 * 0.52*0.52 = 0.064896

P(2 sales) = P(1st sale, 2nd sale, 3rd not) + P(1st not, 2nd sale, 3 sale) + P(1st sale, 2nd not, 3 sale)

= 0.24*(0.52)*(1-0.52) + (1 -0.24)*0.24*0.52 + 0.24*(1-0.52) * 0.24

= 0.1824

So, P(at least 2 sales) = 0.064896 + 0.1824 = 0.247296

Hence, probability is 0.247296 or 0.2473 (approx)

Please comment if any doubt. Thank you.