Problem 521

4. Points $P, Q$ are located on the sides $A B$ and $A C$ of triangle $A B C$ such that $A P: P B=1: 3, A Q: Q C=1: 1$. Point $M$ is chosen on side $B C$ completely at random. Find the probability that the area of triangle $A B C$ does not exceed the area of triangle $P Q M$ by more than six times. Find the expected value of the random variable - the ratio of the areas of triangles $P Q M$ and $A B C$.