Coloured balls are distributed in four boxes as shown in the following table: Box Colour Black White Red Blue I II III IV 3 2 1 4 4 2 2 3 5 2 3 1 6 2 1 3 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.

Explanation

`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))`

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