If from each of the three boxes containing 3 white and 1 black, 2 white and 2 black, 1 white and 3 black balls, one ball is drawn at random, then the probability that 2 white and 1 black balls will be drawn, is

Options

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

Answer

A

Explanation

P(2 white and 1 black)
`P(W_(1)W_(2)W_(3)) orW_(1)B_(2)W_(3) orB_(1)W_(2)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))((2)/(4))((3)/(4)) + ((3)/(4))((2)/(4))((1)/(4))+((1)/(4))((2)/(4))((1)/(4))`
` =(1)/(32) (9 + 3 + 1) = (13)/(32)`