A group of 200 people on the wait-lists for surgery were classified by type of surgery and gender as showsn.

a. If one of the 200 people is randomly selected, what is the probability that the person?

i. Is a female and required orthopedic surgery?

ii. Is a female or requires orthopedic surgery?

iii. Is a female given that orthopedic surgery is required?

b. What value of y in the tables makes the events F(Female) and C(Cardiac surgery) independent? Support your answer with clear probability statements involving F and C.

c. If two different people are randomly selected from this group, what is the probability that only one of them required Cardiac surgery?

Male Female Total Eye Cardiac 48 35 Type of Surgery 83 X y 10 Orthopedic Other 37 22 59 a b 48 Total 120 80 200