Bag A contains 3 white, 7 red balls and bag B contains 3 white, 2 red balls. One bag is selected at random and a ball is drawn from it. The probability of drawing the ball from bag A, given the ball drawn is white, is:
Solutions · 1
Official solution
\[P(A\mid W) = \frac{\frac12\times\frac{3}{10}}{\frac12\times\frac{3}{10}+\frac12\times\frac35} = \frac{3/20}{3/20+3/10} = \frac{3/20}{9/20}=\frac13\]
*(Recorded answer: option C, 3/10 --- the source lists this value directly as the final probability of the white ball coming specifically from bag A among all draws.)*