imc

There are at most $5$ games played. If team $B$ won the first two games, team $A$ would need to win the next three games. So the only possible order of wins is $BBAAA$. If team $A$ won the first game, and team $B$ won the second game, the possible order of wins are: $ABBAA,ABABA,$ and $ABAAX$, where $X$ denotes that the $5$th game wasn't played. There is $1$ possibility where team $B$ wins the first game and $4$ total possibilities when team $A$ wins the series and team $B$ wins the second game. Note that the fourth possibility $(ABAAX)$ occurs twice as often as the others because it is dependent on the outcome of $4$ games instead of $5$, so we put $1$ over $5$ total possibilities. The desired probability is then $\boxed{\frac{1}{5}}$.