There are 3 white, 6 black balls in one bag and 6 white, 3 black balls in second bag. A bag is selected at random and a ball is drawn from it. Find the probability that the ball drawn is black.

Options

A. `3/7`
B. `3/10`
C. `1/4`
D. `1/2`

Answer

D

Explanation

Let `E_(1)=` event of selecting bag first.
`E_(2)=` event of selecting bag second.
`:.P(E_(1))=P(E_(2))=1/2`
Let `E=` event of drawing a black ball.
`:.P(E//E_(1))=6/9=2/3` and `P(E//E_(2))=3/9=1/3`
Now from the total probability theorem,
`P(E)=P(E_(1)).P(E//E_(1))+P(E_(2)).P(E//E_(2))`
`=1/2xx2/3+1/2xx1/3=3/6=1/2`