Serena Williams won the 2010 Wimbledon Ladies Singles Championship. For the seven matches she played in the tournament, her total number of first serves was 379, total number of good first serves was 256, and total number of double faults was 15.

a. Find the probability that her first serve is good.
b. Find the conditional probability of double faulting, given that her first serve resulted in a fault.
c. On what percentage of her service points does she double fault?

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To find the probability that Serena Williams' first serve is good, you need to divide the total number of good first serves by the total number of first serves. Let's calculate it:

a. Probability of a good first serve = Number of good first serves / Number of total first serves
= 256 / 379
≈ 0.6765

Therefore, the probability that Serena Williams' first serve is good is approximately 0.6765, or 67.65%.

To find the conditional probability of double faulting, given that her first serve resulted in a fault, you need to divide the number of double faults after a fault by the number of faults. The formula for conditional probability is:

Conditional probability = Number of double faults after a fault / Number of faults

b. Conditional probability of double faulting = Number of double faults / Number of faults
= 15 / (379 - 256)
= 15 / 123
≈ 0.1219

Therefore, the conditional probability of double faulting, given that her first serve resulted in a fault, is approximately 0.1219, or 12.19%.

To find the percentage of service points where Serena Williams double faults, you need to divide the number of double faults by the total number of service points and then multiply by 100 to get the percentage. The formula is:

Percentage of double faults = (Number of double faults / Total number of service points) * 100

c. Percentage of double faults = (15 / 379) * 100
≈ 3.96

Therefore, on approximately 3.96% of her service points, Serena Williams double faults.