Suppose you have 3 jars with the following contents. Jar 1 has 2 white balls and

Question

Suppose you have 3 jars with the following contents. Jar 1 has 2 white balls and 1 black ball. Jar 2 has 1 white ball and 4 black balls. Jar 3 has 1 white ball and 2 black balls. 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 3, given that the ball is white. What is the probability the ball was drawn from Jar 3, given that the ball is white? (Simplify your answer. Type an integer or a fraction.)

Explanation / Answer

jar 1 = 2W 1B
jar 2=   1W 4B
jar 3=   1W 2B

P(1)=1/3
P(2)=1/2
P(3)=1/6

P(white)=4/11
P(black)=7/11

P(B/A)=P(A intersection B) / P(A)
B=drawn frm jar 3
A=ball is white

P(A intersection B)=1/6 * 1/3
P(A)= 4/11
P(B/A)= 1/18 *11/4 = 11/72

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