The wording of the problem is quite fuzzy.
I'll give you my interpretation.
If we have two teams, where one of the teams has a 55% chance of winning,
how many times must the two teams meet so that we can be 95% certain
that the better team wins at least one game?
Let be the stronger team.
The probability that loses games is: .
. . and we want this to be less than 5%.
So we have: .
Take logs: .
Divide by , a negative quantity: .
. . and we have: .
Therefore, if they play 4 or more matches,
. . we can be 95% certain that will win a game.