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Algebra

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Conditional Probability: Do You Have a Rare Disease?

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Suppose that you are worried that you might have a rare disease. You decide to get tested, and suppose that the testing methods for this disease are correct $99\%$ of the time (in other words, if you have the disease, it shows that you do with $99\%$ probability, and if you don't have the disease, it shows that you do not with $99\%$ probability).

Suppose this disease is actually quite rare, occurring randomly in the general population in only one of every 10,000 people. Find the probability that you indeed have the disease and test positively and round your answer to four decimal places.

A

0.0009

B

0.0090

C

0.0010

D

0.0001