Question

Assume the box contains 9 balls: 3 red, 4 blue, and 2 yellow. A ball is drawn and its color noted. If the ball is yellow, it is replaced; otherwise, it is not. A second ball is then drawn and its color is noted. What is the probability that the first ball was yellow, given that the second was red?

Answer 1

if first ball is a yellow ball, ball is replaced

so, when draw second ball, total ball remains 9

and if it is not yellow,then not replaced then total balls remains in bag =8

so, P(second ball red) = P(first ball yellow and then red) + P(first ball blue and second ball red)+P(first ball red and second ball red) = 2/9*3/9 + 4/9*3/8 + 3/9*2/8

P(first ball was yellow, given that the second was red) = P( first ball was yellow and the second was red) / P(second ball red) = 2/9*3/9 / (2/9*3/9 + 4/9*3/8 + 3/9*2/8) = 0.22857