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Independence Events

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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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Serena is the most likely winner with 35 matches on average, followed by Venus with 33 matches. Cathy is expected to win 22 matches. The numbers are rounded to the nearest whole number.

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