An urn contains 8 white marbles and 5 black marbles. Two marbles are drawn successively from the urn, the first being returned before the drawing of the second. What is the probability that both marbles are black> That both marbles are the same color?
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We're sampling with replacement, so, on any draw, the probability of getting a white marble is 8/13 and the probability of getting a black marble is 5/13, so:
The probability that both marbles are black is (5/13)(5/13), which equals 25/169.
The probability that both marbles are the same color is the probability that both marbles are white, which is (8/13)(8/13), which equals 64/169, plus the probability that both marbles are black, which equals 25/169, as we calculated above. So the total probability is 89/169
The probability that both marbles are black is (5/13)(5/13), which equals 25/169.
The probability that both marbles are the same color is the probability that both marbles are white, which is (8/13)(8/13), which equals 64/169, plus the probability that both marbles are black, which equals 25/169, as we calculated above. So the total probability is 89/169