What is the probability that the person has the disease?

[sahak12]

A certain disease affects about 1 out of 10 000 people. There is a test to check whether the person has the disease.We know that`
•the probability that the test result is positive, given that the person does not have the disease, is only 2 percent
•the probability that the test result is negative, given that the person has the disease, is only 1 percent.
A random person gets tested for the disease and the result comes back positive. What is the probability that the person has the disease?

 

[Deleted member 4993]

A certain disease affects about 1 out of 10 000 people. There is a test to check whether the person has the disease.We know that`
•the probability that the test result is positive, given that the person does not have the disease, is only 2 percent
•the probability that the test result is negative, given that the person has the disease, is only 1 percent.
A random person gets tested for the disease and the result comes back positive. What is the probability that the person has the disease?

Please show us what you have tried and exactly where you are stuck.

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Please share your work/thoughts about this problem.

 

[pka]

You must show us your work so that we will know what sort help you need.

 

[sahak12]

You must show us your work so that we will know what sort help you need.

I`ve tryed to solve this problem and I got this result ((9999 + 98) / 100⁴), but I am not sure.

 

[pka]

I`ve tryed to solve this problem and I got this result ((9999 + 98) / 100⁴), but I am not sure.

Where did you get those numbers?
You want to find \(\mathcal{P}(D|+)\) the probability of having the disease given a positive test result.
So \(\mathcal{P}(D|+)=\dfrac{\mathcal{P}(+|D)\mathcal{P}(D)}{\mathcal{P}(+)}\) Bayes' theorem.

 

[sahak12]

Where did you get those numbers?
You want to find \(\mathcal{P}(D|+)\) the probability of having the disease given a positive test result.
So \(\mathcal{P}(D|+)=\dfrac{\mathcal{P}(+|D)\mathcal{P}(D)}{\mathcal{P}(+)}\) Bayes' theorem.

Thank you very much!!