If from each of the three boxes containing 3 whiter and 1 black, 2 white and 2 black, 1 white and 3 black ball, one bal is drawn at random, then the probability that 2 white and 1 black ball will be drawn is `1//3` b. `1//6` c. `1//2` d. 1/4

Options

A. `(13)/(32)`
B. `(1)/(4)`
C. `(1)/(32)`
D. `(3)/(16)`

Answer

A

Explanation

The contents of three boxes are
`{:(I,3W,1B),(II,2W,2B),(III,1W,3B):}`
Let `W_(i)(i=1,2,3)` be the event of drawing a white ball from ith box and `B_(i)(i=1,2,3)` be the event of drawing a black ball from ith box. Then,
Required probability
`=P(W_(1) cap W_(2) cap B_(3)) cup (W_(1) cap B_(2) cap W_(3))(B_(1) cap W_(2) cap W_(3))`
`=P(W_(1) cap W_(2) cap B_(3)+P(W_(1) cap B_(2) cap W_(3))+P(B_(1) cap W_(2) cap W_(3))`
`=P(W_(1)) P(W_(2)) P(B_(3)) + P(W_(1)) P(B_(2)) P(W_(3))+P(B_(1)) P(W_(2)) P(W_(3))`
`=(3)/(4)xx(2)/(4)xx(3)/(4)+(3)/(4)xx(2)/(4)xx(1)/(4)+(1)/(4)xx(2)/(4)xx(1)/(4)=(26)/(64)=(13)/(32)`