One bag contains 5 white balls and 3 black balls and a second bag contains 2 white balls and 4 black balls. One ball drawn from the first bag and placed unseen in the second bag. What is the probability that a ball now drawn from second bag is black?

Options

A. `15/56`
B. `35/56`
C. `37/56`
D. `25/48`

Answer

B

Explanation

Bag I. has 5 white + 3 black balls.
Bag II. has 2 white + 4 black balls.
`P("Black")_(1st " bag") = 3/8` & `P("White")_(1st " bag") = 5/8`
If one ball is drawn from bag I & placed in bag II, bag II will have 7 balls.
If black ball is drawn, then, bag II contains,
2W + 5 Black balls = 7 balls
P(black ball from bag 1 and black ball from bag 2)
`= 3/8 xx 5/7 = 15/56`
If ball is white then bag II has 3w + 4 black balls P(white ball from bag 1 and black ball from bag 2)
`= 5/8 xx 4/7 = 20/56`
`rArr " Prob(blackball")_("bag"II) = 15/56 + 20/56 = 35/56`