Multiple choice

A bag contains 4 red balls, 5 blue balls, and 6 green balls. If three balls are drawn completely at random from the bag, what is the mathematical probability that all three drawn balls are of identical color?

  1. 34/455

  2. 34/91

  3. 22/455

  4. 12/455

  5. 4/91
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A Correct answer
Explanation

The total number of balls is 15. The number of ways to choose 3 balls is C(15,3) = 455. The number of ways to pick 3 red is C(4,3)=4, 3 blue is C(5,3)=10, and 3 green is C(6,3)=20. The total favorable outcomes are 4+10+20 = 34, so the probability is 34/455.

AI explanation

Using the classical definition of probability, the total ways to draw 3 balls from 15 is 15C3, equaling 455. The favorable outcomes of drawing identical colors are drawing 3 red from 4 (4C3 = 4), 3 blue from 5 (5C3 = 10), and 3 green from 6 (6C3 = 20). The sum of favorable outcomes is 34, making the probability 34/455.

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