Consider two​ boxes, one containing 1 black and 1 white marble​, the other 2 black and 1 white marble. A box is selected at​ random, and a marble is drawn from it at random.  What is the probability that the first box was the one selected given that the marble is​ white? (use a decimal number, rounded to the nearest 1000th. For example, 0.123)

A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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Consider two​ boxes, one containing 1 black and 1 white marble​, the other 2 black and 1 white marble. A box is selected at​ random, and a marble is drawn from it at random.  What is the probability that the first box was the one selected given that the marble is​ white? (use a decimal number, rounded to the nearest 1000th. For example, 0.123)
Expert Solution
Step 1

There are two boxes.

Box 1 contains 1 black and 1 white marble.

Box 2 contains 2 black and 1 white marble.

The probability is the ratio of a number of favorable outcomes of the event to the total number of outcomes.

The conditional probability A given B is given as follows.

P(A|B)=P(AB)P(B)

The intersection probability is 

P(AB)=P(B|A)P(A)

Event B1 is selecting box 1

Event B2 is selecting box 2

Event B is selecting black marble

Event W is selecting box marble

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