50th Mathematical Olympiad in Ukraine, Third Round (January 23, 2010)

There are $6^2=36$ different combinations. Let us calculate the number of cases that satisfy the statement.

Olesya was thrown out $1$, that is impossible.

Olesya was thrown out $2$, the only possible case is $1$.

Olesya was thrown out $3$, possible cases are $1$ and $2$.

Olesya was thrown out $4$, possible cases are $1$, $2$ and $3$.

Olesya was thrown out $5$, possible cases are $1$, $2$, $3$ and $4$.

Olesya was thrown out $6$, possible cases are $1$, $2$, $3$, $4$ and $5$.

Altogether we have $15$ variants. And by definition, the desired probability is $\frac{15}{36}=\frac{5}{12}$.