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If there is 25% chance for event A to happen and there is a 25% chance for event B to happen...What is the % probability for both event A and B to happen.

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    @Alex "... so not so much more additional information" You are missing the point. The information that the events are independent, even though you don't regard it as adding much to the problem, is crucial in that it enables you to solve the problem.2012-09-20

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If they're independent, their probability should have been P(A)*P(B) = $\frac {1}{16}$

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If they are independent, then the probability of both is the product of the two probabilities.

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If they are not independent all you can say is P(A and B)<= min [(P(A), P(B)]. This will be true even if they are independent. I thought that A and B can be constructed to have a certain type of dependence such that any value less than or equal to

min[(P(A), P(B)] possible making it a tight upper bound. But Dilip pointed out that if you choose A and B so that P(A)+P(B)>1 then P(A and B) must be greater than 0 and certainly such A and B can be found..

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    @DilipSarwate thank you for the alternative proof. Because of your two points made in comments I have edited my answer appropriately.2012-09-21