There are three jars that each contain 10 marbles The first

There are three jars that each contain 10 marbles. The first contains 4 white marbles and 6 red marbles, the second 7white and 3 red, and the third all 10 white. An experiment consists of first selecting a jar at random. (Assume each jar has an equal probability of being selected.) After a jar is selected, a marble is randomly drawn from this jar, noting its color. If the marble drawn was white, find the probability that the third jar was selected. (Round your answer to three decimal places.)

Solution

Let

1 = jar 1 is selected
2 = jar 2 is selected
3 = jar 3 is selected
W = white is selected
Thus,

P(3|W) = P(3) P(W|3) / P(W)

As

P(W) = P(1) P(W|1) + P(2) P(W|2) + P(3) P(W|3) = (1/3)(4/10) + (1/3)(7/10) + (1/3)(1) = 7/10

Thus,

P(3|W) = P(3) P(W|3) / P(W) = (1/3)(1) / (7/10) = 5/7

or

P(3|W) =0.476190476 = 0.476 [ANSWER]