White Balls, Black Balls

Probability Level 2

There are two bags AA and BB. Bag AA contains nn white balls and 22 black balls while bag BB contains 22 white balls and nn black balls . One of the two bags is selected at random and two balls are drawn from it without replacement . We know that if both the balls drawn are white balls, the probability of bag AA being selected to draw the balls is 67\frac{6}{7}. Find the value of nn.

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