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Pete and Jimmy (Posted on 2023-12-29) Difficulty: 3 of 5
Old Jimmy and young Pete are both tennis champions. They have played each other many times, each winning exactly half of the matches. When both are fresh Jimmy is much the better player, but he tires rapidly so his probability of winning the kth set is pk, where p is the probability that he wins the first set.

If they always play best-of-five matches, what is the value of p?

See The Solution Submitted by K Sengupta    
Rating: 5.0000 (1 votes)

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Solution I finally figured it out Comment 8 of 8 |
My error was, I was calculating the odds of Old Jimmy winning 50% of the sets instead of 50% of the matches.  (assuming all 5 sets were played in each match even if one player already won 3 -- with my erroneous way of winning 50% of the sets, it may make a difference; I didn't check that)

When I did a (much more complicated) spreadsheet, Goal Seek came up with:
0.777861591369172  (again, not sure to what precision it is accurate)

Edited on January 1, 2024, 2:14 pm
  Posted by Larry on 2024-01-01 14:08:52

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