Multiple choice

If from each of the three boxes containing 3 white and 2 black, 2 white and 3 black and 1 white and 4 black balls, one ball is drawn at random, then the probability that two white and one black ball will be drawn is...

  1. $\dfrac { 37 }{ 125 } $
  2. $\dfrac { 6 }{ 125 } $
  3. $\dfrac { 1 }{ 125 } $
  4. $\dfrac { 36 }{ 125 } $
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A Correct answer
Explanation

Probabilities of drawing white from boxes are 3/5, 2/5, 1/5. Probabilities of black are 2/5, 3/5, 4/5. We need 2 white and 1 black: (W1, W2, B3) + (W1, B2, W3) + (B1, W2, W3) = (3/5*2/5*4/5) + (3/5*3/5*1/5) + (2/5*2/5*1/5) = 24/125 + 9/125 + 4/125 = 37/125.

AI explanation

The probabilities of drawing a white ball from the three boxes are 3/5, 2/5 and 1/5 respectively. To get two white and one black ball, the valid combinations are (white, white, black), (white, black, white) and (black, white, black), which gives the probability expression (3/5 multiplied by 2/5 multiplied by 4/5) plus (3/5 multiplied by 3/5 multiplied by 1/5) plus (2/5 multiplied by 3/5 multiplied by 1/5). Solving this yields 24/125 plus 9/125 plus 4/125, making the total probability 37/125.

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