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In this problem, we have been given three arns and each urn contains a certain number of white balls and a certain number of red balls.
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Now, one ball is selected from each urn.
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We need to find the probability that the ball chosen from urn a was white given that exactly two white balls were selected.
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Now, let us consider the event e to be the event that the ball chosen from the...
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Urn a was white and let us consider f could be the event that exactly two white balls were chosen so if we consider these two events then what we need to find is the probability that the ball chosen from urn a was white given that exactly two white balls were selected.
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So we need to find the probability of e given f.
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And using the definition of conditional probability, this will be equal to p of ef divided by pf.
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So let us determine pef and pf.
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So first of all, let us determine pf.
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So pf means the probability that exactly two white balls.
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Were selected.
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So this will be the number of favorable outcomes by the total number of outcomes.
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Now for the total number of outcomes, we need to select one ball from each urn.
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Now urn a contains two white and four red balls, so that's two plus four which is six balls.
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Earn b contains eight white and four a total of 12 balls and urn c contains one white and three red balls, so a total of 1 plus 3, 4 balls.
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So the total number of ways in which we can select one ball from each urn is obtained by the multiplication rule of counting.
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So we have to multiply these three numbers.
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So this will be our total number of outcomes.
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And in the numerator, we need to write the number of favorable outcomes, which is the number of combinations in which we have exactly two white balls.
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So the first option is that we choose a white ball from urn a.
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There are two ways of doing that.
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Since there are two white balls, which use a white ball from rmb.
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There are eight ways of doing that since there are eight white balls...