Question

There are three boxes, the first one containing 1 white, 2 red and 3 black balls; the second one containing 2 white, 3 red and 1 black ball and the third one containing 3 white, 1 red and 2 black balls. A box is chosen at random, and from it, two balls are drawn at random. One ball is red and the other, white. What is the probability that they come from the second box? Select the correct answer from above options

Answer 1

let A : Ball drawn from bag A B : Ball is drawn from bag B C : Ball is drawn from bag C BB : Black ball WB : White ball RB : Red ball Assuming, selecting bags is of equal probability i.e. \(\frac{1}{3}\) We want to find P(B|WR) i.e. probability of selected White and red ball is from bag B Conclusion: Therefore, the probability of selected white and red ball from bag B is \(\frac{6}{11}\)