Answer:
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!
