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?
.68
a) 379 /256 = .675
c) 67.5 / 15 = 4.5
update.
a) 256/ 379 = .675
a. To find the probability that Serena Williams' first serve is good, we divide the number of good first serves by the total number of first serves.
Probability of good first serve = Number of good first serves / Total number of first serves
Probability of good first serve = 256 / 379
Probability of good first serve ≈ 0.676
b. To find the conditional probability of double faulting, given that her first serve resulted in a fault, we divide the number of double faults after a faulted first serve by the total number of faulted first serves.
Conditional probability of double faulting = Number of double faults after faulted first serve / Total number of faulted first serves
Since the question does not provide the breakdown of faulted first serves, we can't calculate the exact conditional probability.
c. To find the percentage of her service points where she double faults, we divide the number of double faults by the total number of service points and multiply by 100.
Percentage of service points with double faults = (Number of double faults / Total number of service points) * 100
Since the total number of service points is not given, we can't calculate the exact percentage.