Two teams, the Exponents and the Radicals, square off in a best of 5 math hockey tournament. Once a team wins 3 games, the tournament is over.

The schedule of the tournament (for home games) goes: E-R-E-R-E

If the Exponents are playing at home, there is a 60% chance they'll win. If they are playing on the road, there is a 45% chance they'll win.

Find the probability that the Exponents win the series. Round answers to at least 4 decimal places.