12.32 You have torn a tendon and are facing surgery to repair it. The surgeon ex

Question

12.32 You have torn a tendon and are facing surgery to repair it. The surgeon explains the risks to you: infection occurs in 3% of such operations, the repair fails 14% and both infection and failure occur together in 1%. What percent of these operations succeed and free from infection? Follow the four step process in your answer.

12.28 People with type O-negative blood are universal donors. That is any patient can receive a transfusion of O-negative blood. Only 7.2% of the American population have O-negative blood. If 10 people appear at random to give blood, what is the probability that at least 1 of them is a universal donor?

Explanation / Answer

Let I = the event that the operation results in infection, F = the event that the operation fails. We seek P(IC and FC). We are given that P(I) = .03, P(F) = .14, and P(I and F) = .01. Then P(IC and FC) = 1 - P(I or F) = 1 - (.03 + .14 - .01) = .84. b. P(at least 1 is a universal donor) = 1- P(none are universal donors). This is true because we could have 1, 2, 3, 4, 5, 6, 7, 8, 9, or 10. The only outcome left out was 0 or none. P(none) = all 10 are not universal donors = (.928)(.928)(.928)(.928)(.928)(.928)(.928)(.928)(.928)(.928) = .4736742348 1- .4736742348 = .5263

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