I3.2 Two bags $U_{1}$ and $U_{2}$ contain identical red and white balls. $U_{1}$ contains $A$ red balls and 2 white balls. $U_{2}$ contains 2 red balls and $B$ white balls. Take two balls out of each bag. If the probability of all four balls are red is $\frac{1}{60}$, find the value of $B$.
$U_{1}$ contains 2 red and 2 white, total 4 balls. $U_{2}$ contains 2 red and $B$ white, total $2+B$ balls.
$$
\begin{array}{l}
\mathrm{P}(\text { all } 4 \text { are red })=\frac{2}{4} \times \frac{1}{3} \times \frac{2}{2+B} \times \frac{1}{1+B}=\frac{1}{60} \\
20=(2+B)(1+B) \\
B^{2}+3 B-18=0 \\
(B-3)(B+6)=0 \\
B=3
\end{array}
$$