The most complete answer from every reply so far is from Dr. Lena. Thanks for taking the time and going through it!
https://t.co/jGt006Vlh5
You can get the answer using Bayes' theorem, but let's try to come up with it in a different —maybe more intuitive— way.
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Here is what we know:
- Out of 10,000 people, 1 is sick
- Out of 100 sick people, 99 test positive
- Out of 100 healthy people, 99 test negative
Assuming 1 million people take the test (including you):
- 100 of them are sick
- 999,900 of them are healthy
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Let's now test both groups, starting with the 100 people sick:
▫️ 99 of them will be diagnosed (correctly) as sick (99%)
▫️ 1 of them is going to be diagnosed (incorrectly) as healthy (1%)
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Let's now test the group of 999,900 healthy individuals:
▫️ 989,901 of them will be diagnosed (correctly) as healthy (99%)
▫️ 9,999 of them will be diagnosed (incorrectly) as sick (1%)
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Since your test came back positive, it means that you belong to either one of the groups that had a positive result:
1. 99 people that are truly sick, or
2. 9,999 people that are actually healthy (but were diagnosed as sick.)
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Basically, out of 10,098, only 99 are truly sick.
That'll give you a 0.98% chance of being sick!
So no, most likely, you are fine!
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Here is something important: this is true as long as our only priors are that 1 in 10,000 people have the disease.
For example, if you were showing symptoms, then your chance of being sick after receiving a positive test will be higher.