Like most major tennis events, the US open is a single elimination tournament wi

Question

Like most major tennis events, the US open is a single elimination tournament with 128 players entering the first round. A player is eliminated after losing a single match (thus 64 are eliminated after the first round, another 32 after the second, etc). Now assume the following:

i. in any match the probability of the better player winning is 0.8.

ii. the outcome of every match is independent of every other.

iii. how good a player is stays constant throughout the tournament.

What is the probability of the tournament being won by the best player of the 128?

Explanation / Answer

Number of rounds in the tournament = n

2n = 128

n log 2 = log 128

n = 7

So, a player has to win 7 matches to win the tournament'

Probability of the best player winning all the 7 matches he plays = 0.87 = 0.2097

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