Consider a Stanley Cup playoff series (best of seven) where the Toronto Maple Leafs are playing against the Pittsburgh Penguins for the cup
TORONTO
After that:
Toronto hosts the first second and, if needed, fifth and seventh games of the series
The Leafs have a 65% chance of beating the Penguins at home in the first game.
They have a 60% chance of winning home games following a win.
They have a 75% chance of winning home games when bouncing back from a loss.
They have a 30% chance of winning in Pittsburgh after a win.
They have a 55% chance of winning in Pittsburgh after a loss.
What is the probability that the Leafs win in exactly five games?