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)B_(3) or W_(1)B_(2)W_(3) or B_(1)W_(2)W_(3)) `
` =P(W_(1)W_(2)B_(3))+P(W_(1)B_(2)W_(3))+P(B_(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)/(2)*(2)/(4)*(3)/(4) +(3)/(4)*(2)/(4)*(1)/(4)+(1)/(4)*(2)/(4)*(1)/(4)=(1)/(32)(9+3+1)=(13)/(32)`