After your yearly checkup, the doctor has bad news and good news. The bad news i

Question

After your yearly checkup, the doctor has bad news and good news. The bad news is that you tested positive for a serious disease, and that the test is 99% accurate (ie., the probability of testing positive given that you have the disease is 0.99, as is the probability of testing negative given that you dont have the disease). The good news is that this is a rare disease, striking only one in 10,000 people of your age. Why is it good news that the disease is rare? What are the chances that you actually have the disease?

Explanation / Answer

here probability testing postive =P(have disease and tested postive+does nt have disease and tested postive)

=(1/10000)*0.99+(1-1/10000)*(1-0.99)=0.0100098

threfore probability of having disease given tested positive =P(have disease and tested postive)/P(tested postive)

=(1/10000)*0.99/0.0100098=0.00989

as probability of having disease even if tested positive is very less therefore it is good news that disease is rare,

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