There are two bags Bag1 contains 5 white and 3 black balls and bag 2 contains 3 white and 5 - Maths - Probability

Question

There are two bags Bag1 contains 5 white and 3 black
balls and bag 2 contains 3 white and 5 black balls Two balls are
drawn from bag1 and put into bag2 and then two balls are drawn from
bag2 Find the probability that the bals drawn from bag2 are white
and black?

Rishabh Mittal · Accepted Answer

Bag 1: 5 white + 3 black ballsBag 2: 3 white + 5 black ballsCase A: When both transfered balls are blackProbability of drawing both black balls from bag 1 =c23c28Now , No
 of balls in bag 2 = 3 white + 7 black ballsProbability of balls drawn from bag 2 are white and black =c13×c17c210Probability of balls drawn from bag 2 are white and black When both transfered balls are black=c23c28×c13×c17c210=3×3×78×72×10×92=4×9×78×7×10×9=120Case B: When both transfered balls are whiteProbability of drawing both white balls from bag 1 =c25c28Now , No
 of balls in bag 2 = 5 white + 5 black ballsProbability of balls drawn from bag 2 are white and black =c15×c15c210Probability of balls drawn from bag 2 are white and black When both transfered balls are white=c25c28×c15×c15c210=5×42×5×58×72×10×92=2×5×4×5×58×7×10×9=25126Case C: When transfered balls one white and one blackProbability of drawing one white and one black ball from bag 1 =c13×c15c28Now , No
 of balls in bag 2 = 4 white + 6 black ballsProbability of balls drawn from bag 2 are white and black =c14×c16c210Probability of balls drawn from bag 2 are white and black When transfered balls one white and one black=c13×c15c28×c14×c16c210=3×5×4×68×72×10×92=4×3×5×4×68×7×10×9=27

There are two bags.Bag1 contains 5 white and 3 black balls and bag 2 contains 3 white and 5 black balls.Two balls are drawn from bag1 and put into bag2 and then two balls are drawn from bag2. Find the probability that the bals drawn from bag2 are white and black?