2. It is known that bag A contains two red balls and three white balls, and bag B contains three red balls and three white balls. If a ball is randomly drawn from bag A and placed into bag B, and then a ball is randomly drawn from bag B and placed into bag A, the number of white balls in bag A at this point is denoted as $\xi$, then $\mathrm{E} \xi=$ $\qquad$ .
$\begin{array}{l}\text { 2. } \frac{102}{35} . \\ \text { E } \xi=4 \times \frac{2}{5} \times \frac{3}{7}+2 \times \frac{3}{5} \times \frac{3}{7}+ \\ 3\left(1-\frac{2}{5} \times \frac{3}{7}-\frac{3}{5} \times \frac{3}{7}\right) \\ =\frac{102}{35} .\end{array}$