If 1 ball is drawn from each of the boxes `B_1 , B_2 and B_3`, then the probability that all 3 drawn balls are of the same colour , is

Options

A. `(82)/(648)`
B. `(90)/(648)`
C. `(558)/(648)`
D. `(566)/(648)`

Answer

A

Explanation

For i=1,2,3, let `W_(i)(B_(i), R_(i))` denote the event that the ball drawn from `i^(th)` bag is white (black, red).
`therefore` Required probability
`=P{(W_(1) cap W_(2) capW_(3)) cup (B_(1) cap B_(2) cap B_(3)) cup (R_(1) capR_(2) cap R_(3))}`
`=P(W_(1) capW_(2) capW_(3))+P(B_(1)capB_(2)capB_(3))+P(R_(1) capR_(2) capR_(3))`
`=P(W_(1))P(W_(2))P(W_(3))+P(B_(1))P(B_(2))P(B_(3))+P(R_(1))P(R_(2))P(R_(3))`
`=(1)/(6)xx(2)/(9)xx(3)/(12)+(2)/(6)xx(4)/(9)xx(5)/(12)+(3)/(6)xx(3)/(9)xx(4)/(12)=(82)/(648)`