Match Point

The solution of the latest Futility Closet puzzle left me a bit unsatisfied. I understand that the blog usually doesn’t use formulae but in this case, I found the explanation given uncharacteristically hand-wavy. The problem itself is not difficult and I’ll show my solution after the fold.

First things first, here’s the problem:

Henrietta wants a yacht. Her parents think she’s too young. Like all rich people, they settle disagreements by playing competitive lawn tennis.

Henrietta must play three singles matches against her parents. If she wins two matches in a row she gets the yacht. Her mother is a better player than her father. Should she play mother-father-mother or father-mother-father?

My solution: let x the probability of winning against her mother and y the probability of winning against her father. We have: 0

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