3 and show you that it is empty. Similarly, if the prize is in box 3, Monty...
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3 and show you that it is empty. Similarly, if the prize is in box 3, Monty Hall must show you that box 2 is empty. But if the prize is in box 1 (so your initial choice is correct), Monty Hall has a choice of whether to show you box 2 or box 3. Suppose in this case you have probability q2,3 that he chooses box 2, and you have probability q3,2 = 1 − q2,3 that he chooses box 3.
(a) What is your optimal strategy as a function of q2,3?
(b) What is your probability of getting the prize using your optimal strategy?
(c) Show that when q2,3 = q3,2 = 1/2, your optimal strategy and resulting probability of getting the prize coincide with those found in the text for the case p1 = p2 = p3 = 1/3.
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