Question
Suppose you have 3 jars with the following contents. Jar 1 has 1 white ball and...
Suppose you have 3 jars with the following contents. Jar 1 has 1 white ball and 1 black ball. Jar 2 has 4 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 1/3, 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.)
Answers
No. of jars = 3
Jar 1 has 1 white and 1 black ball
Jar 2 has 4 white and 1 black ball
Jar 3 has 1 white and 1 black ball
Probability for selecting jar 3 = P3 = 1/6
Now to select a white (W) ball out of 1W + 1B ball, probability = Pw = 1/2
Hence, the probability the ball was drawn from Jar 3, given that the ball is white = P3*Pw = (1/6)*(1/2) = (1/12)
Hence, answer = 1/12
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