Multiple choice

A bag contains 9 red and 6 white balls. Three balls are drawn at random. The probability that one ball is red and two balls are white is

  1. 27/91

  2. 1/18

  3. 1/27

  4. 1/13
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A Correct answer
Explanation

Total balls = 15. Ways to choose 3 balls = 15C3 = (15*14*13)/(3*2*1) = 455. Ways to choose 1 red (from 9) and 2 white (from 6) = 9C1 * 6C2 = 9 * 15 = 135. Probability = 135/455 = 27/91.

AI explanation

The total number of balls is 15, and the total number of ways to draw three balls is 15C3, which equals 455. The number of ways to draw one red ball out of 9 is 9C1 (which is 9), and the number of ways to draw two white balls out of 6 is 6C2 (which is 15). The probability is the product of these favorable outcomes divided by the total outcomes, giving (9 times 15) / 455, which simplifies to 135/455 or 27/91. The probability is 27/91.

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