Multiple choice

A bag contains 5 green balls and 3 blue balls. If two balls are drawn at random one after another without replacement, what is the probability that both balls are blue?

  1. 3 / 28

  2. 5 / 28

  3. 6 / 27

  4. 9 / 31

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A Correct answer
Explanation

Total balls = 8. Probability of first blue = 3/8. Probability of second blue (without replacement) = 2/7. Total probability = (3/8) * (2/7) = 6/56 = 3/28.

AI explanation

Using the multiplication theorem for dependent events, the probability of drawing a blue ball first is 3 / 8. Without replacement, the probability of drawing a second blue ball from the remaining 7 balls is 2 / 7. The combined probability of both events occurring is (3 / 8) multiplied by (2 / 7), which simplifies to 6 / 56 or 3 / 28.