Multiple choice

In a box, there are eight yellow and four black balls. If three balls are drawn at random, what is the probability that two are yellow and one is black?

  1. 1/16

  2. 28/55

  3. 3/8

  4. 8C2/4C1
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Total balls = 12 (8 yellow, 4 black). Ways to choose 3 balls = 12C3 = (12*11*10)/(3*2*1) = 220. Ways to choose 2 yellow and 1 black = 8C2 * 4C1 = 28 * 4 = 112. Probability = 112/220 = 28/55.

AI explanation

Using the combination formula for probability, the total number of ways to draw 3 balls from 12 is 12C3, which equals 220. The number of ways to choose 2 yellow balls from 8 is 8C2, which is 28, and the number of ways to choose 1 black ball from 4 is 4C1, which is 4, giving 112 favorable combinations. Dividing the 112 favorable outcomes by the 220 total outcomes simplifies to a probability of 28/55.

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