Question

Coloured balls are distributed in four boxes as shown in the following table:A box is selected at random and then a ball is randomly drawn from the selected box. The colour of the ball is black, what is the probability that ball drawn is from the box III?

Answer 1

`P(B_1)=P(B_2)=P(B_3)=P(B_4)`=1/4
E= taking a black ball
`P(E//B_1)`=3/18=1/6
`P(E/B_2)`=2/18=1/14
`P(E/B_3)`=1/7
`P(E/B_4)`=4/13
`P(B_3/E)=(P(E/B_3)P(B_3))/(P(E/B_1)P(B_1)+P(E/B_2)P(B_2)+P(E/B_3)P(B_3)+P(E/_4)P(B_4)`
=`((1/7)(1/4))/((1/6)(1/4)+(1/4)(1/4)+(1/7)(1/4)+(4/13)(1/4))`
=`312/1390`