Consider two boxes: A and B. Box A contains 3 Red and 1 Blue marble. Box B contains 3 Blue and 1 Red marble. Bridget tosses a fair die. If the die comes up with the numbers 1 - 4 then she will choose Box A, if it comes up with 5 or 6, then she chooses Box B. Once a box has been chosen, she will reach inside and randomly pick one of the four marbles in that box. Suppose Bridget shows you that she has picked a red marble. What is the probability that the red marble came from Box B?
A) 1/7.
B) 1/3.
C) 3/4.
D) 1/2.

Question

Quizplus · Accepted Answer

The probability of picking a red marble from Box A is $ \frac{2}{3} \times \frac{3}{4} = \frac{1}{2} $, and from Box B is $ \frac{1}{3} \times \frac{1}{4} = \frac{1}{12} $. The probability that the red marble came from Box B, given that a red marble was picked, is $ \frac{\frac{1}{12}}{\frac{1}{2} + \frac{1}{12}} = \frac{1}{7} $.

Consider Two Boxes: a and B