What is the Probability of Knee Problems Requiring Full Knee Replacement?

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Discussion Overview

The discussion revolves around calculating probabilities related to knee problems and full knee replacements in orthopedic surgery. Participants are working through a problem that includes multiple parts, focusing on the probability of knee issues and the likelihood of requiring a full knee replacement based on given statistics.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Exploratory

Main Points Raised

  • One participant states that 26% of orthopedic surgeries involve knee problems and questions the next steps for calculating probabilities for parts b and c.
  • Another participant suggests that for part b, the probability of requiring a full knee replacement can be derived from the fact that more than two-thirds of knee surgeries involve full replacements.
  • There is a proposal to combine the probabilities for parts b and c, but participants express confusion about how to do this correctly.
  • One participant suggests multiplying 26% by 2/3 for part b, while another corrects them, indicating that the estimate for part b should simply be 2/3, as it pertains to cases involving knee surgery.
  • Participants debate the approach for part c, with one suggesting to use the formula for the probability of both events occurring, while another questions the logic of their calculations, concerned that the resulting probability exceeds the initial probability of a knee problem.
  • Eventually, a participant suggests that the correct approach involves calculating p(knee) multiplied by p(full given knee), leading to a proposed answer of 13/75.

Areas of Agreement / Disagreement

Participants express uncertainty and confusion regarding the calculations for parts b and c, with no consensus reached on the correct methodology until the end of the discussion, where one participant proposes an answer that is acknowledged by another.

Contextual Notes

Participants rely on specific statistics provided in the problem, but there are unresolved questions about the correct application of probability rules and the interpretation of the problem's requirements.

pckofwolfs
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For b and c I have no idea where to go. I know for part b I need the probability of the full knee replacement, but that's all I know. I have no idea what needs to be done for part c. If someone could help that would be greatly apprecieted. I think part a is right. If not could it be explained why it is wrong.According to the American Academy of Orthopedic Surgeons, about 26% of orthopedic surgery
involves knee problems. More than two-thirds of the surgeries involve full knee replacements.
*Round your answer to the nearest percent if necessary*

Age of Adults Getting Knee Replacements
Age Percentage
18-44 2.8%
45-64 24.6%
65-74 43.3%
75-84 26.7%
85-older 2.9%

a) What is the probability that an orthopedic case selected at random involves knee
problems? [1]
The answer I put here was 26%.

b) Of those cases, from part (a), estimate the probability that the case requires full knee
replacement. [1]c) Compute the probability that an orthopedic case selected at random involves a knee
problem and requires a full knee replacement.
 
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pckofwolfs said:
For b and c I have no idea where to go. I know for part b I need the probability of the full knee replacement, but that's all I know. I have no idea what needs to be done for part c. If someone could help that would be greatly apprecieted. I think part a is right. If not could it be explained why it is wrong.According to the American Academy of Orthopedic Surgeons, about 26% of orthopedic surgery
involves knee problems. More than two-thirds of the surgeries involve full knee replacements.
*Round your answer to the nearest percent if necessary*

Age of Adults Getting Knee Replacements
Age Percentage
18-44 2.8%
45-64 24.6%
65-74 43.3%
75-84 26.7%
85-older 2.9%

a) What is the probability that an orthopedic case selected at random involves knee
problems? [1]
The answer I put here was 26%.

b) Of those cases, from part (a), estimate the probability that the case requires full knee
replacement. [1]c) Compute the probability that an orthopedic case selected at random involves a knee
problem and requires a full knee replacement.

Hi pckofwolfs! Welcome to MHB! (Smile)

This looks to be a bit of a trick question.

So of all orthopedic surgeries about 26% involve knee problems.
And of those cases, more than two-thirds involve full knee replacements.
That looks to be the answer to b), doesn't it? (Wondering)

For c) we need to combine those two chances.
How can we combine them to get an answer that makes sense? (Wondering)
 
So for part b would I do something like 26 x (2/3) then subtract that answer from 26 to tell me how many are full knee?
 
pckofwolfs said:
So for part b would I do something like 26 x (2/3) then subtract that answer from 26 to tell me how many are full knee?

No, if we only look at the cases that involve knee surgery, we have over (2/3) knee replacement.
That means that the estimate for b) is simply (2/3).
 
so, for c I'd have (13/50) + (2/3) to be 139/150?
 
pckofwolfs said:
so, for c I'd have (13/50) + (2/3) to be 139/150?

That doesn't look right. (Shake)

The probability of a knee problem is 26%.
How can the probability of a knee problem AND a knee replacement be bigger than that? (Worried)
 
yeah, I have no idea how to do that then. I am taking the AND as a hint to use the and formulas I have say to do p(knee) * p(full). Which you said wouldn't be right.
 
pckofwolfs said:
yeah, I have no idea how to do that then. I am taking the AND as a hint to use the and formulas I have say to do p(knee) * p(full). Which you said wouldn't be right.

Actually, that is (more or less) right!
But that's not what you did...

Properly, it should be p(knee) * p(full given knee).
 
Therefore, 13/75 would be the answer?
 
  • #10
pckofwolfs said:
Therefore, 13/75 would be the answer?

Yep. (Nod)
 

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