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Question
Box I contains two white and three black balls. Box II contains four white and one black balls and box III contains three white ·and four black balls. A dice having three red, two yellow and one green face, is thrown to select the box. If red face turns up, we pick up the box I, if a yellow face turns up we pick up box II, otherwise, we pick up box III. Then, we draw a ball from the selected box. If the ball is drawn is white, what is the probability that the dice had turned up with a red face?
Solution
P(Total) = `1/2 xx 2/5 + 1/3 xx 4/5 + 1/6 xx 3/7`
`=1/5 + 4/15 + 1/14`
`= (42 + 56 + 15)/210`
`= 113/210`
`P(R"/"W) = (P(R).P(W"/"R))/"P(Total)"`
`= (1/2 xx 2/5)/(113/210)`
`= 1/5 xx 210/113`
`= 42/113`
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