Red ball,Black ball
There are two identical boxes namely box 1 and box 2. Box 1 has three red balls and one black ball. Box 2 has two black balls . One ball is randomly taken from box 1 and placed inside box 2 . After this one ball is taken from box 2 and is transferred to box 1 . After these two transfers a red ball is taken out. What is the probability that the red ball is taken out from box 1?
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1 solution
In order for there to be a red ball in box 2 to be drawn, a red ball has to transferred to box 2 with the first transfer (3/4 chance) and then stay in box 2 with the second transfer (2/3 chance.) That means there's a (3/4 * 2/3 = 1/2) chance there even IS a red ball in box 2 when the drawing takes place.
If there is not, there is a 100% chance the red ball was drawn from box 1.
if there is, there is a 2/3 chance (2 red balls in box 1, 1 in box 2) that the red ball was drawn from box 1.
So the total chance of the red ball being drawn from box 1 is (1/2 * 1) + (1/2 * 2/3) = 1/2 + 1/3 = 5/6