Suppose that we have two identical boxes: box 1 and box 2. Box 1 contains 5 red balls and 3 blue balls. Box 2 contains 2 red balls and 4 blue balls. A box is selected at random and exactly one ball is drawn from the box. What is the probability that the ball is blue?
2026-04-24 17:30:24.1777051824
2 boxes and balls, probability question
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Let's divide this into two cases:
Picking box 1 and then a blue ball means the probability of picking box 1 times the probability of picking a blue ball out of box 1, which is 1/2 * 3/8 = 3/16
Picking box 2 and then a blue ball means the probability of picking box 2 times the probability of picking a blue ball out of box 2, which is 1/2 * 4/6 = 1/3
We add the two to get the probability is 25/48