Your doctor has just called you and reported that he has some good news and some

Question

Your doctor has just called you and reported that he has some good news and some bad news. The bad news is that you have tested positive for an exotic disease that will make your head explode. The good news is that the disease is relatively rare, occurring in the general population with a probability of only .001 (i.e., only one in a thousand persons will get the disease). You do some further investigation, and find that, according to the company marketing the test, it's a pretty accurate test. Specifically, the sensitivity of the test is 95 percent (that is, if you have the disease, the probability is.95 that you will test positive). Furthermore, the false positive rate is only five percent (i.e., P(test positive don't have disease) 05). The false negative rate is also just five percent (i.e., P(test negative | have disease)-.05). How worried are you? Your answer should involve Bayes' theorem.

Explanation / Answer

here probability of test result postiive

=P(have disease)*P(test postiive|have disease)+P( do not have disease)*P(test postiive|do not have disease)

=0.001*0.95+(1-0.001)*0.05=0.0509

probability that you have the disease ; given the test result is posiitve =P(have disease|test posiitve)

=P(have disease)*P(test postiive|have disease)/P(test posiitve)

=0.001*0.95/0.0509=0.0187

therefore there is 1.87% chances that you have disease given you are tested positive for disease whcih is not high for you to be very much worried

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