There are two boxes each containing 10 balls. In each box, few of them are black balls and rest are white. A ball is drawn at random from one of the boxes and found that it is black. If the probability that the black ball drawn is from the second box is $\frac{1}{5}$, then number of black balls in the first box is
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This is a classic application of Bayes' Theorem. When you are given a conditional probability like $P(A|B)$ and asked to find the reverse conditional probability $P(B|A)$, Bayes' Theorem is the tool to use.