A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anonymous

  • one year ago

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?

  • This Question is Closed
  1. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    I have a tree diagram started|dw:1439489950303:dw|

  2. kropot72
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    |dw:1439491456952:dw| The first step is to calculate the probability of failure, given that there is infection. \[\large P(F \cap I)=0.005\] \[\large P(F|I)=\frac{P(F \cap I)}{P(I)}=\frac{0.005}{0.02}=0.25\] Then the probability of success, given infection occurs is \[\large P(S|I)=1-P(F|I)=1-0.25=0.75\] Are you able to follow so far?

  3. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Yes, but does it not give you the probability of failure and infection? I thought that's what the '0.5% of the time the repair fails and infection occurs,' meant....

  4. kropot72
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    The probability of success and infection is given by \[\large P(S \cap I)=P(I) \times P(S|I)=0.02\times0.75=0.015\] We are given that the repair fails in 11% of all cases, therefore the overall probability of success is 1 - 0.11 = 0.89 We have found that the probability of success and infection is 0.015. Therefore the probability of success and no infection is 0.89 - 0.015 = 0.875 A corrected drawing follows. |dw:1439493603377:dw|

  5. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    That makes sense..

  6. kropot72
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    That's good :)

  7. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    but at the same time, I can't quite wrap my brain around it. I see what you're saying, and it mathematically makes sense, but I don't quite understand why it is what it is.

  8. kropot72
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    The first step is to find the probability of success in the presence of infection. We are given that the probability of failure in the presence of infection is 0.005 (5%). So we need to use conditional probability theory to find the probability of success in the presence of infection, which is found to be 0.015. It is also effectively given that the overall probability of success (including with and without infection) is 0.89 (1 - 0.11), being 1 minus the overall probability of failure. Now we can separate out the probability of success and no infection, by simply subtracting 0.015 from 0.89. Giving 0.875.

  9. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Just to see if I followed this properly, the missing number at the end, which would be infection+success would be 0.105|dw:1439495124441:dw|

  10. kropot72
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    No so. The probability that the operation is successful and infection-free is already on the probability tree, being 0.875.

  11. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Isn't the decimal of a percent such as 5%, 0.05 rather than 0.005 ??

  12. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Isn't 0.005 0.5%?

  13. kropot72
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    And the probability of infection plus success is also on the tree, being 0.015. The probability of failure and no infection was not on my diagram. the reason being that it is not asked for. "Isn't 0.005 0.5%". Yes it is, that is the conversion from a percentage to a probability.

  14. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Okay, thank you for your help. (:

  15. kropot72
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    |dw:1439495695074:dw|

  16. kropot72
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    You're welcome :)

  17. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.