There are 3 bags which are known to contain 2 white and 3 black, 4 white and 1 black, and 3 white and 7 black ball, respectively. A ball is drawn at random from one of the bags and found to the black ball. Then the probability that it was drawn from the bag containing the most black ball is a.`7//15` b. `5//19` c. `3//4` d. none of these

Options

A. `7//15`
B. `5//19`
C. `3//4`
D. None of these

Answer

A

Explanation

Consider the following events.
A: ball drawn is black
`E_(1):` bag I is chosen
`E_(2):` bag II is chosen
`E_(3):` bag III is chosen
Then, `P(E_(1))=(E_(2))=P(E_(3))=1/3`
`P(A//E_(1))=3/5,P(A//E_(2))=1/5,P(A//E_(3))=7/10`
Therefore, the required probability is
`P(E_(3)//A)=(P(E_(3))P(A//E_(3)))/(P(E_(1))P(A//E_(1))+P(E_(2))P(A//E_(2)))=7/15`
`" "+P(E_(3))P(A//E_(3))`