Answer: C. 81/125
Step-by-step explanation:
The games is over in 3 sets. For Fred to win the match there are 3 possibilities.
1) Fred wins the first 2 sets with probability (3/5)^2
2)Fred wins the first set. Looses the next set. Wins the third set.
(3/5)(2/5)(3/5)
3)Fred looses the first set. Wins the next 2 sets.
(2/5)(3/5)(3/5)
The probability that Fred wins is the sum of the above 3 probabilities . That means that the probability that Fred wins the match is
(3/5) ^2 +(3/5) ^(2)(2/5) + (3/5) ^(2)(2/5) = 81/125
