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 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 drawn is white what is the probability that the dice had turned up with a red face

Explanation

let the event of getting white balls be W

let the event of getting red face up be R

probability of red face `=3/6`

required probability = `(3/6 * 2/5)/((3/6*2/5)+(2/6*4/5)+(1/6*3/7))`

`=(1/5)/(1/5+4/15+1/14)`

`=(1/5)/((42+56+15)/210)`

`=1/5*210/113`

`= 42/113` answer