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Will you change your box? Why or why not?

+1 vote
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You are presented with three boxes. One of them has a red ball inside and the other two have a black ball inside each of them. You are asked to pick up the one with red ball and you pick one. Now, one of the other boxes is opened and it is found to have a black ball.

You are presented with a chance to change your box with the one that is left closed. Will you change your box? Why or why not?

posted Mar 27, 2015 by Rajni

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1 Answer

+1 vote

The probability of the box taken has a red ball is 1/3
Whereas, the Probability that it was inside one of the other two boxes that was not picked up is 2/3.
When one was taken out, it was black. So that box was ruled out. Now the other unopened box has the probability that the box has a red ball = 2/3 .
So, you must exchange the box with the other unopened box so that probability of that being red is high

answer Apr 2, 2015 by Muthulakshmi K



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