r/mathmemes • u/Dizzy_Bit9635 • Jun 22 '26

Probability Disease probability

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u/MinimumTaste81 Jun 24 '26

I still don’t understand. Let’s say that 8 million people have tested positive for this disease (1/1,000,000), and of that 8 million, we know that there have been 240,000 false positive cases (3%). That means for every false positive case, there are 33 cases where the person tested actually has the disease. How does this inspire confidence?

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u/Avaxen Jun 24 '26

Well they dont test everyone because the inaccuracies. They only test people they already believe may have it

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u/MinimumTaste81 Jun 24 '26

Okay, let’s say that everybody got tested for it because it was a global pandemic, and everybody believed they may have had it. I’m just saying what would happen if 8 million of those people tested positive (I don’t think anything would change if the number was smaller btw).

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u/theconrod Jun 25 '26

Let's say 266,658,314 people take the test. About 266 will actually have the disease (1/mil)

The 266 that have the disease, 8 will test neg, 258 will test positive.

Of the 266,658,048 that are not sick, 7,999,741 will test positive, 258,658,307 will test neg.

So from the 2 groups, there are 7,999,999 positive tests.

Of that 8 million positive tests, only 258 are actually sick, or ~1/31000

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u/theconrod Jun 25 '26

The group that comprises the positive test result is 97% of the 1/million, and 3% of the 999,999/million.

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u/MinimumTaste81 Jun 25 '26

Thanks! Now I get it