Reference no: EM131529926

Question: On the TV show "Let Make a Deal," one of the three boxes (A, B, C) on the stage contains keys to a Lincoln Continental. The other two boxes are empty. A contestant chooses box B. Boxes A and C remain on the table. Monty Hall, the energetic host of the show, suggests that the contestant surrender her box for $500. The contestant refuses. Monty Hall then opens one of the remaining boxes, box A, which turns out to be empty. Monty now offers $1000 to the contestant to surrender her box. She again refuses but asks whether she can trade her box B for box C on the table. Monty exclaims, "That's weird." But is it really weird, or does the contestant know how to calculate probabilities? Hint: Suppose that there are n boxes. The probability that the key is in any of the (n - 1) boxes on the stage = (n - l)/n. Monty opens p boxes, which turn out to be empty. The probability that the key is in any of the (n - p - 1) boxes is (n - 1)/ n(n - p - 1). Without switching, the probability that the contestant wins remains at lin. Hence it is better to switch. In this case n = 3, p = 1. The probability of winning without a switch is 1. The probability of winning by switching is 2/3.