Question

Microfracture knee surgery has a 79% chance of success of patients with degenerative knees. The surgery is performed on 13 patients. a. Find the probability that the surgery is successful on all of the patients. b. Find the probability that the surgery is successful on at most 10 patients.

Answer 1

p=probability of success of surgery = 0.79

n= number of patients taken = 13

X= number of patients having a successful surgery

Thus X~Binomial(n=13, p=0.79) [ since there is n number of trials and probability of success equal to p)

           x=0,1,,,,,,,,,,13

13 0.79"(0.21)13- P(X x)

a)

P(surgery is successful on all patients) = P(X=13)

130.79 (0.21)1-18 P(X 13) 0.04668229

b)

P(surgery is successful on atmost 10 patients) = P(X<=10) = 1-P(X>10) =1-P(X>=11)

13 P(X 21) -Σ() 0.79"(0.21) 13-r r-11 = 0.4652970

So,

P(X10 1 - P(X> 10)1 P(X 11) 1 0.4652970 = 0.5347030