# math

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.

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1. 0.0194

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if E wins they can do it with:

0 losses
1 loss
2 losses

for how many combinations can they do each of the above
start there

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3. if E wins, they can do it with:

0 losses out of 3 games: C(2,0) = 1 way to do that, since the last game must be a win

1 loss out of 4 games: C(3,1) = 3 ways to do that, since the last game must be a win

2 losses out of 5 games: C(4,2) = 6 ways to do that, since the last game must be a win

thus, there are 10 total ways to win the tournament, each with its own probability

for example, the probability of winning in 3 games is: 0.6 * 0.45 * 0.6 = 0.162

do that same calculation for each of the 10 ways to win – be careful whether the individual game is home or away – then sum the probabilities across all 10 ways

you should get 0.5756

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