Statistical probability of being sick

Question

You have a machine that has a $0.9$ probability to give the correct diagnosis of a flu disease (similar for both the negative and positive diagnoses).
The probability of having the disease is $0.01$ for the general public. You know that a person sampled from the population was diagnosed as positive for the flu by this medical device.
Given this observation, what is the probability of that person having the disease?
I have no idea how to solve this, I think the population follows a normal distribution, but I can't think of anything. I would like you to explain to me what I should do. Thank you!

Henry · Accepted Answer

Hint:
Suppose you had $1000$ people.

How many would you expect to have the disease?

How many of those would you expect to test positive?

How many would you expect to not have the disease?

How many of those would you expect to test positive?

So how many in total would you expect to test positive?

What proportion of those testing positive would you expect to have the disease?

Statistical probability of being sick

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