Sunday, October 2, 2016

If n people are tested positive for an illness with x probability of accuracy, how confident are we that you are sick?

Yet another way of explaining Bayes's conditional probability.

I found this from Hilary Mason, who in turn heard it from Jake Hofman and Chris Wiggins.

If there are 10,000 people.
1% are sick.
The test has a 99% confidence of accuracy
Given a positive result, what is the probability that you are sick?

10% of 10,000 is 100 - 100 people test positive. 99% accuracy means that we expect 99 people to be sick and not the whole 100.

But also, of the remaining 10,000 - 100 people, 99% will have tested incorrectly so 1% of that group will be ill. 1% of 9900 = 99.

So in total, we have 99 sick people testing positive
And 99 healthy people being positive.

So, if you test positive you have a 50% chance of being sick.

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