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"Stuck b/w joint probablity and conditional probability"

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Say there is a rare disease that affects 1 person in 100,000. We develop a test for it, but it's not perfect: It has no false negatives, but it has a 1% chance of testing positive on patients that don't have the disease.

You can make a table like this:

               SICK   HEALTHY

POSITIVE     0.00001  0.0099999

NEGATIVE     0        0.9899901

The numbers in that table are joint probabilities (e.g., the probability that someone is healthy and gets a negative result in the test).

Now, if you test positive and want to know what's the probability that you are sick, the number you are looking for is called the conditional probability of being sick given that you tested positive. That number is 0.00001/(0.00001+0.0099999) = 0.00099901...


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