Multiple choice

A bag contains 5 black and 4 white balls. Two balls are drawn at random. The probability that they match is

  1. $\displaystyle \frac{7}{12}$
  2. $\displaystyle \frac{5}{8}$
  3. $\displaystyle \frac{5}{9}$
  4. $\displaystyle \frac{4}{9}$
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D Correct answer
Explanation

Total ways to draw 2 balls = 9C2 = 36. Ways to draw 2 black = 5C2 = 10. Ways to draw 2 white = 4C2 = 6. Total matching ways = 10 + 6 = 16. Probability = 16/36 = 4/9.

AI explanation

The total number of ways to draw two balls from the bag containing 9 balls is 9C2, which equals 36. The probability that the two balls match in color means either both are black or both are white; the number of ways to choose 2 black balls is 5C2, which is 10, and the number of ways to choose 2 white balls is 4C2, which is 6. The total number of favorable outcomes is 10 plus 6, which is 16, making the probability 16 divided by 36, or 4/9.

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