Multiple choice

A bag contains 4 red balls, 5 green balls, and 3 blue balls. Two balls are drawn one after another without replacement. What is the probability that both balls are of different colors?

  1. 69/77

  2. 47/66

  3. 66/77

  4. 60/77

  5. 68/77

Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Total balls = 12. P(same color) = P(RR) + P(GG) + P(BB) = (4/12 * 3/11) + (5/12 * 4/11) + (3/12 * 2/11) = (12 + 20 + 6) / 132 = 38/132 = 19/66. P(different) = 1 - 19/66 = 47/66.

AI explanation

The total number of balls is 12, so the probability of drawing two balls of the same color is the sum of ways to draw red, green or blue pairs divided by the total pairs. This gives 4C2 plus 5C2 plus 3C2 equals 6 plus 10 plus 3, totaling 19 favorable pairs, while 12C2 equals 66 total pairs. The probability of same colors is 19 divided by 66, so the probability of different colors is 1 minus 19 divided by 66, which equals 47 divided by 66.