10. As shown in the figure, given the parabola $y^{2}=2 p x(p>0)$ with focus $F$ and directrix $l$, a line through point $F$ intersects the parabola at points $A, B$, and $|A B|=3 p$. Let the projections of points $A, B$ on $l$ be $A^{\prime}, B^{\prime}$, respectively. If 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
Answer $\frac{1}{3}$.
Analysis
The required probability $=\frac{S_{\triangle A^{\prime} B^{\prime} F}}{S_{\text {trapezoid } A A^{\prime} B^{\prime} B}}=\frac{\left|A^{\prime} B^{\prime}\right| \cdot p}{\left|A^{\prime} B^{\prime}\right| \cdot\left(\left|A A^{\prime}\right|+\left|B B^{\prime}\right|\right)}=\frac{\left|A^{\prime} B^{\prime}\right| \cdot p}{\left|A^{\prime} B^{\prime}\right| \cdot(|A F|+|B F|)}=\frac{\left|A^{\prime} B^{\prime}\right| \cdot p}{\left|A^{\prime} B^{\prime}\right| \cdot 3 p}=\frac{1}{3}$