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 greater than 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. `3//7`
B. `4//7`
C. `6//17`
D. `8//17`

Answer

B

Explanation

`(b)` Let `A` be the event of drawing a black ball.
`A_(1)`, the event of choosing the first box.
`A_(2)`, the event of choosing the second box.
`:.P(A_(2)//A)=(P(A//A_(2))*P(A_(2)))/(P(A//A_(1))*P(A_(1))+P(A//A_(2))*P(A_(2)))`
`=((4)/(7)*(1)/(2))/((3)/(7)*(1)/(2)+(4)/(7)*(1)/(2))=((4)/(7))/(1)=(4)/(7)`