Question

Three urns contain respectively $3$ white and $1$ black balls, $2$ white and $2$ black; $1$ white and $3$ black. One ball is selected at random from each urn, Find the chance that the three selected comprise $1$white and $2$ black balls in form of $\frac{k}{32}$.

Answer 1

The event may happen in any of the following mutually exclusive ways: $WBB,BWB,BBW$.
The probabilities of these are $\frac{3}{4}.\frac{2}{4}.\frac{3}{4},\frac{1}{4}.\frac{2}{4}.\frac{3}{4},\frac{1}{4}.\frac{2}{4}.\frac{1}{4}.$respectively.
Required probability is their sum $=\frac{26}{64}=\frac{13}{32}$