Multiple choice

A bag contains 6 white and 4 black balls. Two balls are drawn at random and one is found to be white. The probability that the other ball is also white is

  1. $\displaystyle \frac{2}{13}$
  2. $\displaystyle \frac{5}{13}$
  3. $\displaystyle \frac{8}{13}$
  4. $\displaystyle \frac{9}{13}$
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B Correct answer
AI explanation

The problem requires finding the conditional probability that both balls are white given that at least one is white, calculated as P(both white) / P(at least one white). The probability of drawing two white balls from 6 is 6C2 divided by 10C2, which equals 15/45 or 1/3. The probability that at least one ball is white is found by subtracting the probability of drawing two black balls (4C2 / 10C2 = 6/45) from 1, yielding 39/45 or 13/15. The resulting conditional probability is (1/3) / (13/15), which equals 5/13.

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