Three sisters : Venus , Serena , and the well-hidden little Cathy, play one tennis opponent per week. The chances of each sister beating any unrelated player are 7/10, 8/10, and 9/10, respectively. The probabilities of any sister beating another are given in the table

/ v s c

v .0 .6 .7

s .4 .0 .9

c .3 .1 .0

(for example Venus beats Cathy 7/10 of the time).

Each week, one pair of sisters plays each other (at random) ; the third plays an outsider. In a 50-match season, which player is likely to win the most matches, and how many matches would each one expect to win, on the average?

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