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

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In summary, the probability of an orthopedic case involving a knee problem is 26%, and of those cases, more than two-thirds involve full knee replacements. To compute the probability of an orthopedic case involving both a knee problem and a full knee replacement, we multiply the probability of a knee problem (26%) by the probability of a full knee replacement given a knee problem, which is approximately 17.3% (2/3 of 26%). This gives us an estimated probability of 13/75 or approximately 17.3%.
  • #1
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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  • #2
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)
 
  • #3
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?
 
  • #4
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).
 
  • #5
so, for c I'd have (13/50) + (2/3) to be 139/150?
 
  • #6
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)
 
  • #7
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.
 
  • #8
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).
 
  • #9
Therefore, 13/75 would be the answer?
 
  • #10
pckofwolfs said:
Therefore, 13/75 would be the answer?

Yep. (Nod)
 

1. What is the probability of developing knee problems?

The probability of developing knee problems varies depending on several factors such as age, weight, physical activity level, and previous injuries. However, according to the American Academy of Orthopaedic Surgeons, the overall prevalence of knee osteoarthritis in the United States is approximately 14% in adults aged 25 and older.

2. Are certain populations more at risk for knee problems?

Yes, certain populations are more at risk for knee problems. These include individuals who are overweight or obese, older individuals, athletes who participate in high-impact sports, and those with a family history of knee problems.

3. Can knee problems be prevented?

While some knee problems may be unavoidable, there are steps that can be taken to potentially reduce the risk. These include maintaining a healthy weight, wearing appropriate footwear during physical activity, and performing exercises to strengthen the muscles around the knee joint.

4. How do you calculate the probability of a knee injury?

The probability of a knee injury can be estimated by taking into account factors such as age, physical activity level, and previous injuries. However, it is important to note that calculating the exact probability of an injury is not possible and should not be relied upon for making decisions about physical activity.

5. Can knee problems be treated?

Yes, knee problems can often be treated with a combination of conservative methods such as physical therapy, medication, and lifestyle changes. In some cases, surgery may be necessary to address more severe knee problems.

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