Question

You have a torn tendon and are facing arthroscopic surgery to fix it. The surgeon explains the risks of the surgery. Infection occurs in 2% of all cases and the repair fails in 11% of the cases. 0.5% of the time the repair fails and infection occurs. What is the probability that the operation is successful and infection-free?

Answer 1

@jim_thompson5910

Answer 2

P(Operation Successful and infection free) = P( (Operation does NOT fail) and (Infection does NOT occur) )


P(Operation Successful and infection free) = P(Operation does NOT fail) * P(Infection does NOT occur)


P(Operation Successful and infection free) = (1 - P(Operation fails)) * (1 - P(Infection))


P(Operation Successful and infection free) = (1 - 0.11) * (1 - 0.02)


P(Operation Successful and infection free) = (0.89) * (0.98)


P(Operation Successful and infection free) = 0.8722


This sounds right, but I'm not sure how/where the 0.5% fits in

Answer 3

Ok so the answer would be the .8722 part?

Answer 4

let me draw a probability tree real quick to make sure

Answer 5

ok

Answer 6

hmm i can only get part of the tree done, and not the part I want

Answer 7

maybe a tree won't work here

Answer 8

Do u think the .87 etc is the right answer

Answer 9

@jim_thompson5910

Answer 10

yeah i don't have any other reason to doubt it, just not sure how the 0.5% fits in or why they put it there