Multiple choice

A bag contains 5 red balls and 4 green balls. If 4 balls are drawn at random, what is the probability that exactly 2 balls are red and 2 balls are green?

  1. 10 21

  2. 7 21

  3. 1 21

  4. 5 21

  5. None of these
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A Correct answer
Explanation

The number of ways to choose 2 red balls from 5 is C(5,2) = 10. The number of ways to choose 2 green balls from 4 is C(4,2) = 6. Total ways to choose 4 balls from 9 is C(9,4) = 126. Probability = (10 * 6) / 126 = 60 / 126 = 10 / 21.

AI explanation

The bag holds 9 balls, making the total ways to draw 4 balls equal to 9C4, which is 126. The favorable ways to draw exactly 2 red and 2 green balls are calculated by multiplying 5C2 and 4C2, yielding 10 times 6 for 60 favorable outcomes. The probability is 60 divided by 126, which simplifies to 10/21.

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