Two dice whose larger value is exactly four

Two fair six-sided dice are thrown. What is the probability that the larger of the two numbers shown equals $4$?

$7/36$. The maximum is at most $4$ with probability $(4/6)^2$ and at most $3$ with probability $(3/6)^2$. The difference, $\tfrac{16-9}{36}=\tfrac{7}{36}$, is the chance the maximum is exactly $4$.