Suppose you have 3 jars with the following contents. Jar 1 has 1 white ball and

Question

Suppose you have 3 jars with the following contents. Jar 1 has 1 white ball and 1 black ball. Jar 2 has 2 white balls and 1 black ball. Jar 3 has 1 white ball and 1 black ball. One jar is to be selected, and then 1 ball is to be drawn from the selected jar. The probabilities of selecting the first, second, and third jars are 1/2, 1/3, and 1/6 respectively. Find the probability the ball was drawn from Jar 1, given that the ball is white. What is the probability the ball was drawn from Jar 1, given that the ball is white? Simplify your answer. Type an integer or a fraction.)

Explanation / Answer

There is 1 white ball and 1 black ball in the 1st jar so that the probability of drawing a white ball from the 1st jar, when the 1st jar is selected , is ½. Hence, the probability that a white ball is drawn from the 1st jar = the probability of selecting the 1st jar * the probability that a white ball is drawn from the 1st jar = (1/2)*(1/2) = ¼.

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