Question

A bag contains 2 yellow shirts, 4 red shirts, 3 green shirts, and 3 blue shirts. Find the probability of choosing a blue shirt, then choosing another blue shirt without replacing the first one.

A) P(Blue, Blue) = 3/12 * 2/11

B) P(Blue, Blue) = 3/12 * 3/11

C) P(Blue, Blue) = 3/12 * 4/11

D) P(Blue, Blue) = 2/12 * 3/11

Answer 1

The probability of choosing a blue shirt, then another blue shirt without replacing the first one from a bag containing multiple colored shirts, is 3/12 * 2/11. This is because there are initially 3 blue shirts out of 12, and then 2 blue shirts out of 11 after one is removed. Therefore, the correct answer is A) P(Blue, Blue) = 3/12 * 2/11.

Step-by-step explanation:

When calculating the probability of choosing two blue shirts one after the other without replacement from a bag containing 2 yellow shirts, 4 red shirts, 3 green shirts, and 3 blue shirts, we must consider that the first event affects the second. The total number of shirts is 2 + 4 + 3 + 3 = 12. The probability of choosing a blue shirt the first time is 3 out of 12, or 3/12. After taking one blue shirt out, we are left with 2 blue shirts out of a total of 11 shirts, since one shirt has been removed. Therefore, the probability of choosing another blue shirt is now 2 out of 11, or 2/11. We multiply these probabilities together to find the combined probability of both events occurring in sequence:

P(Blue, Blue) = (3/12) * (2/11)

This can be simplified to:

P(Blue, Blue) = 1/4 * 2/11 = 1/22

Therefore, the correct answer is A) P(Blue, Blue) = 3/12 * 2/11.