4. According to the problem, the random variable $\xi=\frac{C M}{C B}$ is uniformly distributed on the interval $[0 ; 1]$. If $x$ is the value of the random variable $\xi$, then

$$
\mathrm{s}(x)=\mathrm{S}_{P Q M}=S_{A B C} \cdot\left(1-\frac{1}{6}-\frac{3 x}{4}-\frac{(1-x)}{3}\right)=\frac{S_{A B C}}{12}(6-5 x) \rightarrow \frac{\mathrm{S}_{P Q M}}{S_{A B C}} \geq \frac{1}{3}
$$

Then the condition $\frac{S_{P Q M}}{S_{A B C}} \geq \frac{1}{3}$ takes the form

$$
\frac{6-5 x}{12} \geq \frac{1}{3}
$$

From this, we find $x \leq \frac{2}{5}$. Considering the uniform distribution, $P(A)=\frac{2}{5}$.

Let's find the expected value of the random variable $X=\frac{S_{P Q M}}{S_{A B C}}$

$$
M_{X}=\int_{0}^{1} \frac{6-5 x}{12} d x=-\left.\frac{1}{120}(6-5 x)^{2}\right|_{0} ^{1}=\frac{7}{24}
$$
Answer: 1) $\left.P(A)=\frac{2}{5} ; 2\right) M_{X}=\frac{7}{24}$.