Suppose John has a torn tendon and is facing surgery to repair it. The surgeon explains the risks to John: infection occurs in 4 % of operations, the repair fails in 12 % of operations, and both infection and failure occur together in 0.78 % of operations. What percentage, P , of these operations succeed and are free from infection? Please round your answer to the nearest two decimal places. P = %

The probability of not having an infection and the surgery being a success is 0.8478.

Step-by-step explanation:

Hello!

There are several possible outcomes facing surgery to repair a torn tendon:

"Infection" ⇒ P(In)= 0.04

"Repair fail" ⇒ P(F)= 0.12

"both infection and failure" ⇒ P(In∩F)= 0.0078

P(NIn∩S)=?

Where NIn represents "no infection" and S represents "successful surgery"

The event "no infection" is complementary to the event "infection" and so is it's probability P(NIn)= 1 - P(In)= 1 - 0.04= 0.96

The event "successful surgery" is complementary to the event "Repair fail" and so is it's probability: P(S)= 1 - P(F)= 1 - 0.12= 0.88

                         "Repair fail"      ;  "successful surgery";  Total

"Infection"       :   P(In∩F)           ;         P(In∩S)               ;     P(In)

"no infection" :  P(NIn∩F)         ;         P(NIn∩S)            ;     P(NIn)

                                P(F)            ;                P(S)              ;         1

P(F)   = P(In∩F) + P(NIn∩F)  

P(NIn∩F)  =   P(F)  - P(In∩F) = 0.12 - 0.0078= 0.1122

P(NIn∩S)= P(NIn) - P(NIn∩F) = 0.96-0.1122= 0.8478

The probability of not having an infection and the surgery being a success is 0.8478.

I hope it helps!

answer: the dogs need to shift their focus to human scent.

its because the dogs being trained are for search and rescue thus they need to be able to track humans and their specific scent