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Anders_H comments on Open Thread, Jun. 8 - Jun. 14, 2015 - Less Wrong
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I am assuming you want the posterior probability of disease given three positive tests. You're going to need more information - unless you provide either the specificities or the likelihood ratios, the question cannot be answered.
I may have used weak phrasing.
Each test returns positive. The frequency out of 20 go's that each does so correctly is indicated respectively by the "12," "16," and "12.5."
So really, it's the odds of actually having the disease, given the three positive test results, I guess. Would it be 1/2 under those circumstances?
Thank you for your assistance.
You also need to consider the odds of a false positive for each test.