Multiple choice

Bag A contains three black balls and one white ball, Bag B contains two black balls and two white balls, Bag C contains one black ball and three white balls. One ball is drawn randomly from each bag. What is the probability that one of them is black and the other two are white?

  1. 3/32

  2. 13/32

  3. 1/32

  4. 3/2

  5. None of the above
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The probability of drawing one black and two white balls is the sum of the probabilities of three mutually exclusive scenarios: (B, W, W), (W, B, W), and (W, W, B). Bag A: P(B)=3/4, P(W)=1/4. Bag B: P(B)=2/4, P(W)=2/4. Bag C: P(B)=1/4, P(W)=3/4. Calculating: (3/4 * 2/4 * 3/4) + (1/4 * 2/4 * 3/4) + (1/4 * 2/4 * 1/4) = 18/64 + 6/64 + 2/64 = 26/64 = 13/32.

AI explanation

Using the multiplication rule for independent events, the probability of drawing exactly one black and two white balls is the sum of three mutually exclusive cases. Calculating each case gives (3/4 times 2/4 times 3/4) + (1/4 times 2/4 times 3/4) + (1/4 times 2/4 times 1/4), which equals 18/64 + 6/64 + 2/64. Adding these fractions gives a total probability of 26/64, which simplifies to 13/32.

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