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Find the probability if you change your choice in the "Price is right" gane show given...

Find the probability if you change your choice in the "Price is right" gane show given your first choice is incorrect
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Answer #1

There are three doors, and only one has a big prize. You are asked to choose one, and you do. The probability of choosing the big prize is, of course, 1/3. That means that there is a 2/3 chance that you chose the wrong door.

Now you are given the chance to change your choice. Your original choice had a probability of being the big prize at 1/3. The other two doors combined had a probability of 2/3 combined. However, one of those two doors was already shown to you as the not-selected door with no big prize. That means that the remaining other doors now holds the probability of the two doors. That is, the remaining not-selected door has a 2/3 probability of being correct.

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