# Thread: Probability: A person is in considerable pain with a non-life threatening condition.

1. ## Probability: A person is in considerable pain with a non-life threatening condition.

Im not sure how to go about working this out or explaining it. I actually think a 10% chance of dying is high.

Should she have the operation?

Even though we are dealing with uncertainty, we still use probability to make decisions. Here is a real example.
A person is in considerable pain with a non-life threatening condition. She is deciding whether or not to have an operation to fix her problem. She has been told that the chance of her dying as a result of the operation is 10%

• What does the “10%” mean in this context?
• What are the pros and cons of having this operation?
• What factors would you consider if you were in this situation?

2. I can address only the first question directly:

#1 -- We RARELY hear information like this. ALMOST ALWAYS, the doctor would rather report the 90% chance of living. It is the same thing from a mathematical point of view.

#2 -- It is false and misleading information. The individual will either die or live. One cannot die only 10%. What the number actually means is that there is a history for this procedure and so far, 10% of people undergoing the procedure have died. Each individual is either in "die" or "live". One simply doesn't know until after the procedure.

#3 -- This is a standard misunderstanding of population data. Population data MUST NOT be applied to individuals. It is WRONG to do so. Having said that, U.S. Courts do it all the time. Over some large number of cases, this manages to create some measure of social equity, but it does not, in any way, do the exactly correct thing for ANY individual.

#4 -- There is also an important statistical argument about frequentists vs Bayesians. This is an important discussion, but the patient facing the procedure probably doesn't care about it. The patient just wants to be in the "live" group. Nether side of the argument can promise that.

3. Originally Posted by missy_muffett
Im not sure how to go about working this out or explaining it. I actually think a 10% chance of dying is high.

Should she have the operation?

Even though we are dealing with uncertainty, we still use probability to make decisions. Here is a real example.
A person is in considerable pain with a non-life threatening condition. She is deciding whether or not to have an operation to fix her problem. She has been told that the chance of her dying as a result of the operation is 10%

• What does the “10%” mean in this context?
• What are the pros and cons of having this operation?
• What factors would you consider if you were in this situation?
tkhunny well expressed several of the thorny issues that come up in trying to interpret what probability means in real life.

If I assume that this is an exercise you were given in an introductory probability class, then you are probably expected not to think quite so deeply, but just to apply to this question whatever you have been taught as the definition of probability (and then, in the last two parts, perhaps you see for yourself what that definition is not fully adequate).

Can you tell use what you have learned as the definition, and apply that to this 10%?

4. ## Probability : Operation

Hello Dr Peterson,

we learned about probability from a 5 minute online lecture, then read a chapter in a book called 'The Tiger that isnt' & have to work out our own answers.
This basically seems how the uni is running its maths course, every week new concept, short lecture read the book answer 10 questions. Therefore to try &
make sense of what I should be doing, I am looking for someone to help me along the way & explain what I need to be doing.

5. Originally Posted by missy_muffett
Hello Dr Peterson,

we learned about probability from a 5 minute online lecture, then read a chapter in a book called 'The Tiger that isnt' & have to work out our own answers.
This basically seems how the uni is running its maths course, every week new concept, short lecture read the book answer 10 questions. Therefore to try &
make sense of what I should be doing, I am looking for someone to help me along the way & explain what I need to be doing.
So, what did the lecture and the chapter say about probability that might be useful here? In particular, do they give a definition of probability that you can apply? Or, since it appears that the book is an informal presentation of ideas and may not formally define probability, are there any examples given that suggest how you should think of the phrase "the chance of her dying as a result of the operation is 10%"?

Be sure to talk with your instructor if you are having trouble understanding your responsibilities in the course or feel you need additional resources. The course is designed for you to succeed, but some students need help in adapting to a particular unfamiliar style, and teachers are ready to help them.

6. Originally Posted by missy_muffett
Hello Dr Peterson,

we learned about probability from a 5 minute online lecture, then read a chapter in a book called 'The Tiger that isnt' & have to work out our own answers.
This basically seems how the uni is running its maths course, every week new concept, short lecture read the book answer 10 questions. Therefore to try &
make sense of what I should be doing, I am looking for someone to help me along the way & explain what I need to be doing.
What was the book chapter about? Did it clarify anything?

What my approach would be considering the way new material is introduced to you:
1. Look for "introduction to <insert your topic>" videos on youtube. E.g. I've heard Khan Academy videos are good.
2. After watching a video or 2 look for "basic/beginner <insert your topic> exercises" or try to answer the 10 questions.
3. If something is not clear ask here.

Regarding the 3 questions, it seems the 2nd and 3rd don't require a deep understanding of probability. What do you get from the operation? What's the downside? What would you consider when faced with a similar choice?

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