A group of 200 people on the waitlists for surgery were classified by type of su

Question

A group of 200 people on the waitlists for surgery were classified by type of surgery and gender as shown. Type of Surgery Eye Cardiac Orthopedic Other Total 48 35 37 120 Male Female Total 80 83 10 59 48 200 a. If one of the 200 people is randomly selected, what is the probability that the perso (6 marks) i. Is a Female and requires Orthopedic surgery? ii. Is a Female or requires Orthopedic surgery? ii. Is a Female given that Orthopedic surgery is required? What value of y in the table makes the events F (Female) and C (Cardiac surgery) independent? Support your answer with clear probability statements involving F and C. (3 marks) b. If two different people are randomly selected from this group, what is the probability that only one of them required Cardiac surgery? (3 marks)

Explanation / Answer

i) P(female and require Orthopedic) =22/200 =11/100 =0.11

ii) P(female or require Orthopedic) =(80+59-22)/200=0.585

iii) P(female|Orthopedic) =22/59=0.3729

b)

for Female and cardiac surgery to be independent:

P(F)*P(C) =P(F and C)

(80/200)*(10/200)=y/200

y=4

c)

P(one cardiac surgery) =P(1st one has and 2nd one has not+1st one has not and 2nd one has )

=(10/200)*(190/199)+(190/200)*(10/199) =0.0955

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