Bayes’ theorem: "A man goes to see his medical doctor to find out..."

elsmee

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Bayes’ theorem: "A man goes to see his medical doctor to find out..."

Hi all

Ive been trying to solve this problem for hours but cannot work it out for the life of me. Any assistance would be greatly appreciated.

A man goes to see his medical doctor to find out whether or not he has a deadly disease. The test is positive. The test is 95% accurate and one in one thousand men of his age has this disease. What is the probability he has the disease?

He decides to seek a second opinion but the results are exactly the same. When this question was put to a group of doctors, 80% of them answered “95%”.
He now plans to sell up all his assets, tell his boss what he really thinks of her, quit his job on the spot and live in Mauritius in the time he has left. Is this a rational decision? Explain.

Regards
ElSmee
 
I did my working in excel but every time I try and link the images my post won't show on the forum. I calculated the probability that he has the disease to be 1.9%.
However I don't understand the significance of the statement that [FONT=&quot]When this question was put to a group of doctors, 80% of them answered “95%”[/FONT]
 
I agree with your answer. My calculations show 1.866...%, but rounding it to 1.9% could be an acceptable answer, depending on your teacher's preferences. As for the bit that's confusing you, it doesn't really mean a whole lot. It can be taken at face value. A panel of doctors were asked to solve the same problem you were tasked with, to use Bayes' Theorem to determine how likely it is the man is really sick. 80% of the doctors answered by saying the odds were 95% that the man had the disease. So, essentially, that bit can be ignored. It merely sets the stage to explain why the man is now planning to sell everything he owns and await his death. The question asks you to assess, based on what you know, whether that's a wise plan or not.
 
Hi all

Ive been trying to solve this problem for hours but cannot work it out for the life of me. Any assistance would be greatly appreciated.

A man goes to see his medical doctor to find out whether or not he has a deadly disease. The test is positive. The test is 95% accurate and one in one thousand men of his age has this disease. What is the probability he has the disease?

How I would do this: imagine 100000 people who take this test. 100 of them have the disease, 100000- 100= 99900 do not. Of the 100 who have the disease .95(100)= 95 text positive, 100- 95= 5 do not. Of the 999000 people who do not have the disease, 99900(.05)= 4995 test positive, 99900- 4995= 94905 do not. Of the 4995+ 95= 5090 who test positive for the disease, 5 of them have it. Given that the man tested positive for the disease the probability he actually has the disease is 5/5090= 0.0009.

He decides to seek a second opinion but the results are exactly the same. When this question was put to a group of doctors, 80% of them answered “95%”.
He now plans to sell up all his assets, tell his boss what he really thinks of her, quit his job on the spot and live in Mauritius in the time he has left. Is this a rational decision? Explain.

Regards
ElSmee
Of course, its a rational decision! Moving to Mauritius and living on the beach for the next 50 years of your life is always a good decision!
 
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