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 2 white balls 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 1/3, 1/2, and 1/6 respectively. Find the probability the ball was drawn from Jar 2, given that the ball is white. What is the probability the ball was drawn from Jar 2, given that the ball is white? (Simplify your answer. Type an integer or a fraction.)

Explanation / Answer

Jar 1 -- 1white ball and 1 black ball

Jar 2 -- 2 white ball and 1 black ball

Jar 3 -- 2 white ball and 1 black ball

P(selecting Jar 1) = 1/3

P(selecting Jar 2) = 1/2

P(selecting Jar 3) = 1/6

P(white ball) = (1/3)(1/2)+(1/2)(2/3)+(1/6)(2/3) = (3+6+1)/18 = 10/18

P(jar 2 / white ball) = P(jar 2 and white ball)/P(white ball)

= (1/2)(2/3)/(10/18) = 6/10 = 0.6

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