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 p
k, 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?
(In reply to
I see my error by Larry)
Even if they played all 5 sets each time,
regardless, that would not affect the probability
that Jim would win matches half the time
(needing 3 or more sets out of 5 to win a match).
Also, my interpretation of your formula was not correct. Now I don't
know what it represents. For example, the likelihood of
Jim winning 5 sets in a row is p^15 not p^5.
But, your formula comes very close to giving the right answer. :-)
Edited on December 29, 2023, 10:53 pm
re: I see my error
