A diagnostic test has been developed for a rare disease, which affects 1 in 1000

Question

A diagnostic test has been developed for a rare disease, which affects 1 in 1000 people. Suppose that the test gives a positive result 95% of the time when an individual has the disease, and gives a positive result 1% of the time when the individual does not have the disease. (a) 4 pts Suppose an individual is tested and the result is positive. What is the probability that they have the disease? (b) 6 pts Suppose another individual is given two completely separate tests (you may assume that they are conditionally independent given the disease state D). What is the probability that this person has the disease, given that both tests were positive? How does this answer compare to part (a)

I couldn't' quite figure out part b

Explanation / Answer

b) probability that both test are positive =P(have disease and both test positive+do not have disease and both test positive) =(1/1000)*0.95*0.95+(999/1000)*0.01*0.01=0.001002

therefore probability that this person has the disease, given that both tests were positive =

P(have disease and both test positive)/P(both test positive) = =(1/1000)*0.95*0.95/0.001002 =0.900699

this is very much higher in comparison to part (a) and provide higher relaibility.

please revert for any clarification required.

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