Will I make it to Wimbledon

Probability Level 2

I booked center court tickets for the Wimbledon Men's Final best-of-five match. As luck would have it, I got stuck in traffic and now I cannot make it to the court before the match starts. However, I will certainly be able to make it just before the start of the fifth set (if there is one).

If each player has a 50% chance of winning each set, what is the probability that I would miss the match completely (with no fifth set played)?


The answer is 0.625.

Janardhanan Sivaramakrishnan by Janardhanan Sivaramakris… , 42

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2 solutions

Stephen Mellor
Nov 11, 2017

Assume that even if the match ends after 3 sets, a fourth is played anyway. Thus the possible combinations of wins are:

AAAA AAAB BBBA BBBB AABA ABAA BAAA BBAB BABB ABBB

AABB ABAB BAAB BBAA BABA ABBA

10 out of the 16 mean missing the match, hence the probability is 5/8, meaning the answer is 625.

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I don't get why a 4th set is played anyways. I counted the possibilities to get to 3-0,3-1,0-3 and 1-3. This are 2 ways for the 3-0 and 6 for the 3-1.

Peter van der Linden - 3 years, 6 months ago

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I assumed that a fourth was played, which allowed me to calculate the probability easier. Say, for example, that you were drawing a probability tree to represent this information. If you didn't assume that a fourth set was played, you would have some branches ending after 3 events and some ending after 4 events. If you weren't to assume a fourth set anyway (the result having no bearing), you would have to remember to count the branches ending after 3 events twice, which I presume is where you tripped up.

Stephen Mellor - 3 years, 6 months ago

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Aah that makes it clearer. The way it was represented is was like... Uhm yeah, and Uhm why. But it's the same

Peter van der Linden - 3 years, 6 months ago

AAAB or AAAA are not possible outcomes. So the branch would indeed end after AAA.

Michael Vogt - 3 years, 6 months ago

What? You didn't even put how many possible 5set-games can be played. How can you calculate the probability of the game not making to the 5th set if you didn't even have a 5th set. Also, I cannot accept the AAAA and BBBB, four games streak wins? When the game is best of five (first who can 3 wins)?

I counted the game's possible outcome. 3 sets - 2 games. 4 sets - 6 games. 5 sets - 12 games.

20 possible outcomes of the game. 8 games are not 5sets. 8/20 = 40%

Patrick Labra - 3 years, 6 months ago

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The question asks what is the probability that the match will be missed. By counting up to the fourth set, that is all that is required.

Stephen Mellor - 3 years, 6 months ago

One possibility is that the game ends in 3 matches, i.e. a single player wins each match. For player A, the probablity is (1/2)^3 or 1/8. So the probability that one of the players wins each match is 1/4. Now, for the remaining 3/4 possibility if three matches are played without a winner, that means one player has won 2 matches and the other has won 1. The probability of the player who has won two matches already is 1/2. So this means that for the remaining 3/4 possibilities that more than three matches are played, there is a 1/2 chance it will end in the next match => (1/2)*(3/4)=3/8

Add this to the 1/4 possibility that the game will be over in three matches => 1/4 + 3/8 = 5/8 or 62.5%

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