Multiple choice

A bag contains 7 green and 8 white balls. If two balls are drawn simultaneously, the probability that both are of the same colour is -.

  1. 7/15

  2. 6/12

  3. 3/12

  4. 4/15

  5. None of the above
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A Correct answer
Explanation

Total balls = 15. Ways to pick 2 = 15C2 = 105. Ways to pick 2 green = 7C2 = 21. Ways to pick 2 white = 8C2 = 28. Total favorable = 21 + 28 = 49. Probability = 49/105 = 7/15.

AI explanation

The total number of balls is 15, so the total ways to draw two balls simultaneously using the combinations formula is 15C2 = 105. The number of ways to draw two green balls is 7C2 = 21, and the number of ways to draw two white balls is 8C2 = 28. The probability of drawing same colors is (21 + 28) / 105 = 49/105, which simplifies to 7/15.

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