Multiple choice

There are three blue marbles, four red marbles, six green marbles and two yellow marbles. When three marbles are drawn what is the probability that one is yellow and two are red?

  1. 24/455

  2. 3/91

  3. 12/455

  4. 15/91

  5. none of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Total marbles = 3+4+6+2 = 15. Ways to choose 3: 15C3 = (15*14*13)/(3*2*1) = 455. Ways to choose 1 yellow (2C1) and 2 red (4C2): 2 * 6 = 12. Probability = 12/455.

AI explanation

The total number of marbles is 15, so the total ways to draw 3 marbles is 15C3, which equals 455. The favorable outcomes require drawing 1 yellow from 2 and 2 red from 4, calculated as 2C1 times 4C2 for 2 times 6, giving 12 ways. Dividing the favorable outcomes by the total outcomes gives a probability of 12/455.

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