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

for something like this, I would draw out a probability tree

Answer 2

Here's how I got those numbers

first there's a 0.5% chance that there's an infection and the repair fails, so if you get an infection, then there's a 0.5/2 = 0.25 = 25% chance the repair fails

so there's a 75% chance it doesn't fail meaning that the probability of getting an infection and not having the repair fail is 0.02*0.75 = 0.015 = 1.5%

Answer 3

it says that 11% of the cases result in repairs failing, so the remaining bit must be 11 - 0.5 = 10.5%

finally, all the values in the very far column must add to 100%, so

0.5 + 1.5 + 10.5 + x = 100

12.5 + x = 100

x = 100 - 12.5

x = 87.5

and that explains how I got the answer of 87.5%

Answer 4

hopefully that makes sense

Answer 5

ohhh. yeah, it does. thanks so much!!

Answer 6

you're welcome