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
Solution by Larry)
While small, the differences between our two solutions is significant.
I agree that your resulting p, when put back into your equation,
does more accurately add to 2.5, but I question whether this formula
is the right one. The best I can understand your equation is this:
If Jim and Pete were playing by some non-standard rules:
play up to 5 sets and stop as soon as Sam loses.
Count the number of sets he has won.
If the expectation value of the number of sets he wins is 2.5,
(half the sets) then this is the p you have solved for.
Edited on December 30, 2023, 3:07 am
re: Solution
