three boxes b1b2b3 contains balls with diferent colours whit

three boxes b1,b2,b3. contains balls with diferent colours white2,1,2 black 3,2,4 red 4,3,2
white black red I 2 1 2 II 3 2 4 III 4 3 2

a die is throw is chosenb1 if either 1 or2 turns up.b2 is chosen if 3or4 tuns up.b3 is chossen if 5or6turs up having choosen a box. if the ball drawn is found to be red,find the propablithy that is from box b2   

Solution

The box B1 has 2 white, 3 black and 4 red balls. The box B2 has 1 white, 2 black and 3 red balls and the box B3 has 2 white, 4 black and 2 red balls.

To choose between the boxes, a dice is tossed. If 1 or 2 turns up, box B1 is chosen; if 3 or 4 turns up, box B2 is chosen and if 5 or 6 turns up , box B3 is chosen.

A ball is drawn and found to be red in color. The total number of red balls is 9, the number of red balls in box B2 is 3.

The probability that the ball is from box B2 is 3/9 = 1/3.