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# Probability question

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Two teams, team A and team B, are playing in a best 2 out of 3 tournament. Team A has a 60% chance of winning any game. What is the probability that team A wins the tournament?

Sep 2, 2021

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This probability problem is simple enough that it seems directed towards a brute force method, which is what I will use.

Let's first write out all the ways that team A could win the tournament, then sum the probabilities.

By games that would have been won:

A-B-A

B-A-A

A-A

You might be scratching your head at only having 2 games with the A-A permutation, but in this case, the third game doesn't matter, and might not be played in some tournament formats. Thus, we only need to calculate for until team A wins.

A-A = 60% * 60% = 36%

A-B-A = 60% * 60% * 40% = 36% * 40% = 14.4% (substitution from A-A chance calculation)
B-A-A = 14.4% by the commutative property of multiplication, it's the same as A-B-A

36%

+ 14.4%

+ 14.4%

=======

64.8%

Therefore, Team A has a 64.8% chance of winning the tournament.

Sep 2, 2021