Bag I contains 3 red and 4 black balls and Bag II contains 4 red and 5 black balls. One ball is transferred from Bag I to Bag II and then a ball is drawn from Bag II. The ball so drawn is found to be red in colour. Find the probability that the transferred ball is black.

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)`