5. Suppose that you are worried that you might have a rare disease. You decide t

Question

5. 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 percent of the time (in other words, if you have the disease, it shows that you do with 99 percent probability, and if you don't have the disease, it shows that you do not with 99 percent probability). Suppose this disease is actually quite rare, occurring randomly in the general population in only one of every 10,000 people 10 pt You obtain a positive test result. What is the probability that you have the disease? [Hint: Use Bayes Rule]

Explanation / Answer

It is given that ONLY 1 IN EVERY 10,000 PEOPLE have this rare disease occurring randomly.
Since the testing method is only 99% correct. Hence we can safely assume that it is 1% incorrect.
Hence, in 1,000,000 people, 100 will show the disease, out of these 100, 1 will be diagnosed incorrectly.
However, out of the remaining 999,900 non-disease people, 9,999 will be shown to have the disease as well.
Hence, the probability of actually having contracted the disease = 99 / (99+9999) = 0.0098 ANSWER

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