One the game show Lets Make a Deal, you are shown three doors, A, B, and C, and
ID: 3154125 • Letter: O
Question
One the game show Lets Make a Deal, you are shown three doors, A, B, and C, and behing one of them is the Big Prize. After you select one of them- say, door A- to make things more intersting the host (Monty Hall), who knows what is behind each door opens one fo the doors- say, door B- to reveal that the Big Prize is not there. He then offter you the opportunity to change your selection to the remaining foor, door C.
Suppose there are 1000 doors. you select door A and Monty, knowing what is behing each door opens all but one of the doors. (Let's say he does not open door B) revealing the Big Prize is not behind any of those doors. Monty offers you the opportunity to change your selection to door B. SHould you change your selection to door B?
If you switch, the probability of winning the Big Prize is__________________?
If you do not switch, the probability of winning the Big Prize is ________________?
Explanation / Answer
If you switch, the probability of winning the Big Prize is__________________?
You are with 2/3 probability wrong when you chose A. Hence, when you switch, you have probability winning of
P(win|switch) = 2/3 [ANSWER]
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If you do not switch, the probability of winning the Big Prize is ________________?
You are with 1/3 probability right when you chose A. Hence, when you don't switch, you have probability winning of
P(win|no switch) = 1/3 [ANSWER]
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