A bag contains 4 white and 2 black balls, and another bag contains 3 white and 5 black balls. If one ball is drawn from each bag, find the probability that one is white and the other black.

Solution

In first bag, there are 4 white and 2 black balls ; in second bag there are 3 white and 5 black balls. P (one white ball and one black ball) = P (‘one white ball from first bag and one black ball from second bag’ or ‘one black ball from first bag and one white ball from second bag’)
= P (one white ball from first bag and one black ball from second bag) + P (one black ball from first bag and one white ball from second bag)
$equals space 4 over 6 cross times 5 over 8 plus 2 over 6 cross times 3 over 8 space equals 20 over 48 space plus space 6 over 48 space equals space 26 over 48 space equals space 13 over 24$

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Probability

A bag contains 4 white and 2 black balls, and another bag contains 3 white and 5 black balls. If one ball is drawn from each bag, find the probability that one is white and the other black.

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