. Bag A contains 4 red, 3 white and 2 black balls. Bag B contains 3 red, 2 white and 3 black balls. One ball is transferred from bag A to bag B and then a ball is drawn from bag B. The ball so drawn is found to be red. Find the probability that the transferred ball is black. ans is 2/33 i want the solution

bag A contains 4 red, 3 white and 2 black balls. bag B contain 3 red, 2 white and 3 black balls. one ball is transferred from bag A to bag B and then a ball is drawn from bag B. the ball so drawn is found to be red. find the probability that the transferred ball is black.

let E1,E2 and E3 be the event that transferred ball is red,white and black respectively.

let A be the event of getting red ball.

by Bayes theorem:

case 1: when red ball is transferred from bag A to bag B,

number of balls in bag A = 9, number of red ballsin bag A=4

probability of transferring red ball =4/9,

after transferring red ball number of red balls in bag B=3+1=4,

therefore probability of selecting red ball from bag B=4/9

when transferred ball is red

case 2: when white ball is transferred:

Probability of transferring white ball from bag A=3/9

after transferring white ball to bag B, probability of selecting red ball from bag B=3/9

when event E2 occured

similarly

hence the required probability