Multiple choice

A bag contains 5 red and 7 black balls. Two balls are drawn at random. Probability both are of the same color is:

  1. 30 66

  2. 31 66

  3. 32 66

  4. 33 66
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Total balls = 12. Ways to pick 2 balls = 12C2 = 66. Ways to pick 2 red = 5C2 = 10. Ways to pick 2 black = 7C2 = 21. Total favorable = 10 + 21 = 31. Probability = 31/66.

AI explanation

The total number of ways to draw 2 balls from 12 is 12 choose 2, which equals 66. The number of ways to draw 2 red balls from 5 is 5 choose 2, which is 10, and the number of ways to draw 2 black balls from 7 is 7 choose 2, which is 21. The probability of drawing balls of the same color is the sum of these two favorable outcomes divided by the total, giving 10 plus 21 divided by 66, which is 31 divided by 66.

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