Given two bags A and B follows: bag A contains $$3$$ red and $$2$$ white balls and bag B contains $$2$$ red and $$5$$ white balls. A bag is selected at random, a ball is drawn and put into the other bag, and then a ball is drawn from the second bag. The probability that both balls drawn are of the same color is

Question

Given two bags A and B follows: bag A contains $$3$$ red and $$2$$ white balls  and bag B contains $$2$$ red and $$5$$ white balls. A bag is selected at random, a  ball is drawn and put into the other bag, and then a ball is drawn from the  second bag. The probability that both balls drawn are of the same color is

Infinity Learn · Accepted Answer

The whole event consists of the following mutually exclusive ways.(1) Selecting the bag A, drawing a red ball from A and putting it into bag B and then drawing a red ball from B.(2) Selecting the bag A, drawing a white ball from A and putting it into bag B and then drawing a white ball from B.(3) Selecting the bag B, drawing a red ball from B and putting it into A and then drawing a red ball from A.(4) Selecting the bag B, drawing a white ball from B and putting it into A and then drawing a white ball from A.The required probability is $$=12$$×$$35$$×$$38+12$$×$$25$$×$$34+12$$×$$27$$×$$23+12$$×$$57$$×$$12$$                                                 $$=980+320+221+528=9011680$$

Given two bags A and B follows: bag A contains 3 red and 2 white balls and bag B contains 2 red and 5 white balls. A bag is selected at random, a ball is drawn and put into the other bag, and then a ball is drawn from the second bag. The probability that both balls drawn are of the same color is

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