Barb finds that the tennis in the park is not as competitive as she would like. So she goes to a local community center when she wants to play tennis. There are usually 12 or 13 players who show up. They use playing cards that they choose at random to divide up into three different courts of four for each set.
There is one player who comes every day who is not good enough to play with such a competitive group. Barb told me that she seems to be in his foursome more often than everyone else. In fact, she decided to play pickleball in another community instead of tennis because on this problem.
A few days ago, she decided to take her friend Barb to the community center to play tennis with the group. That one player who seems to always ruin her foursome was there as usual. Barb played four sets and, even though the foursomes were selected randomly, that fellow was in her foursome every time.
Barb came home and asked if I could calculate the probability of that happening.
I figured that there were 495 ways to choose a foursome out of 12 players.
There are 45 ways to have any two players in the same foursome.
So there would be a probability of 45/495=0.09 of Barb and that fellow being in the same foursome. So she should expect to play with him once every 1/0.09=11 sets or once every 11/4=2.75 days.
The probability of Barb and that fellow being in the same foursome four times a row would be 0.09^4=0.00007. So she should expect to play on the same foursome four times in a row once every 1/0.00007=14,641 days.
Barb wasn't sure whether this fact meant that she should buy a lottery ticket or not.
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