Question

A bag $X$ contains $4$ white balls and $2$ black balls, while another bag $Y$ contains $3$ white balls and $3$ black balls. Two balls are drawn (without replacement) at random from one of the bags and were found to be one white and one black. Find the probability that the balls were drawn from bag $Y.$

Answer 1

Bag $X$ contains $4$ white balls and $2$ black balls , Bag $Y$ contains $3$ white balls and $3$ black balls.

Number of ways of selecting $1$ white ball and $1$ black ball from bag $X$ is $4\times 2=8$ ways.

Number of ways of selecting $1$ white ball and $1$ black ball from bag $Y$ is $3\times 3=9$ ways.

Total number of ways is $8+9=17.$

The probability that the balls are drawn from bag $Y$ is $\frac{9}{17}.$