Multiple choice

A bag contains $8$ red and $5$ white balls. Three balls are drawn at random. Find the probability that one ball is red and two balls are white.

  1. $\displaystyle\frac{40}{143}$
  2. $\displaystyle\frac{40}{147}$
  3. $\displaystyle\frac{41}{141}$
  4. $\displaystyle\frac{39}{147}$
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A Correct answer
Explanation

The total number of ways to choose 3 balls from 13 is 13C3 = 286. The number of ways to choose 1 red ball from 8 is 8C1 = 8, and 2 white balls from 5 is 5C2 = 10. The probability is (8 * 10) / 286 = 80 / 286 = 40 / 143.

AI explanation

The total number of ways to draw 3 balls from 13 balls (8 red and 5 white) is 13C3, which equals 286. The number of ways to choose 1 red ball out of 8 is 8C1, and the number of ways to choose 2 white balls out of 5 is 5C2, giving 8 times 10 = 80 favorable combinations. Using the classical definition of probability, the probability is 80 divided by 286, which simplifies to 40/143.

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