10. As shown in Figure 1, the parabola $y^{2}=2 p x(p>0)$ has a focus at $F$ and a directrix at $l$. A line passing through point $F$ intersects the parabola at points $A$ and $B$, and $|A B|=3 p$. Let the projections of points $A$ and $B$ on $l$ be $A^{\prime}$ and $B^{\prime}$, respectively. A point $M$ is randomly thrown into the quadrilateral $A A^{\prime} B^{\prime} B$. The probability that point $M$ falls within $\triangle F A^{\prime} B^{\prime}$ is $\qquad$
10. $\frac{1}{3}$.

The required probability is
$$
\begin{array}{c}
\frac{S_{\triangle A^{\prime} B^{\prime} F}}{S_{\text {trapezoid } A A^{\prime} B^{\prime} B}}=\frac{\left|A^{\prime} B^{\prime}\right| p}{\left|A^{\prime} B^{\prime}\right|\left(\left|A A^{\prime}\right|+\left|B B^{\prime}\right|\right)} \\
=\frac{p}{(|A F|+|B F|)}=\frac{p}{3 p}=\frac{1}{3} .
\end{array}
$$