8. There are 25 balls in total in two boxes, each ball being either white or black. If one ball is drawn from each box, the probability that both balls are black is $\frac{27}{50}$. Find the probability that both balls are white.
8. Let the first box contain $n$ balls, $b$ of which are black; then the second box contains $(25-n)$ balls, with $B$ being black. Then $\frac{b B}{n(25-n)}=\frac{27}{50} . \therefore n(25-n)$ is a multiple of 5, $\therefore n$ is a multiple of 5.
Let $n=5$ or 10 (otherwise swap the boxes), if $n=5$ then $b B=54, \therefore b$ ! 54 and $b \leqslant 5 . \therefore b=1,2,3$.
Verification: $B=54,27,18$. Only $B=18 \leqslant 20$ meets the condition. $\therefore b=3, B=18 \quad P=\frac{2}{5} \cdot \frac{1}{10}=\frac{1}{25}$. If $n=10, b B=81, \therefore b=B=9, \therefore P=\frac{1}{10} \cdot \frac{2}{5}=\frac{1}{25}$. In summary: $P=\frac{1}{25}$.