Multiple choice

A bag contains 3 different white balls, 4 different black balls and 2 different red balls. Two balls are picked at random. Find the probability of picking (a) one white ball and one red ball, (b) no white ball, and (c) exactly one black ball.

  1. a - 1 6 , b - 5 36 , c - 5 12

  2. a - 5 6 , b - 21 36 , c - 5 9

  3. a - 1 6 , b - 5 12 , c - 5 9

  4. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Total balls = 9. Total ways to pick 2 = 9C2 = 36. (a) 1 white (3C1) and 1 red (2C1) = 3 * 2 = 6. Prob = 6/36 = 1/6. (b) No white (6 non-white balls) = 6C2 = 15. Prob = 15/36 = 5/12. (c) Exactly one black (4C1 * 5C1) = 20. Prob = 20/36 = 5/9.

AI explanation

The bag holds 9 total balls, so picking 2 yields a sample space of 9C2, which equals 36. Using the combination method for probability, the chance for one white and one red is (3C1 times 2C1) divided by 36, giving 6/36 or 1/6. The chance for no white balls is 6C2 divided by 36, which is 15/36 or 5/12. The chance for exactly one black ball is (4C1 times 5C1) divided by 36, yielding 20/36 or 5/9. The probability values are 1/6, 5/12, and 5/9.

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