A box contains `4` white and `3` black balls. Another box contains `3` white and `4` black balls. A die is thrown. If it exhibits a number `ge 3`, the ball is drawn from the first box. Otherwise, a ball is drawn from the second box. A ball drawn is found to be black. The probability that it has been drawn from the second box is

Options

A. `1//2`
B. `6//7`
C. `4//7`
D. `3//7`

Answer

D

Explanation

Box `I to 4W, 3B`
Box `II to 3W, 4B`
Probability for choosing first box=`(3)/(6)=(1)/(2)`
Probability for chossing second box=`(1)/(2)`
`therefore` Required probability=`((3)/(14))/((3)/(14)+(4)/(14))=((3)/((14)/(7)))/((7)/(14))=(3)/(7)`