probability qestion

Question

in class we showed that if 1/1000 people have a disease and the probability that a test for disease gives the correct result 95% of the time then the probability that a randomly selected person has the disease is only 0.02 .However, poor Alicia was probably tested because she had symptoms. Suppose that 0.1 people with Alicia symptoms have the disease.
A-Compute the probability that Alicia has the disease given her symptoms.




B- Compute the relative risk for a person with symptoms and a positive test compared a randomly selected person with a positive test and provide an interoperation.

Answer 1

P(d/s) = .1 = probability one with symptoms has the disease

test for disease is 95% accurate P(d/s) = .95

0.1% has the disease or .2%?? the given information seems contradictory. do 1 in a thousand or 2 in a thousand have the disease??

maybe you meant P(s/d) = .1 and find P(d/s). then use Bayes Theorem

P(d/s)= P(s/d)P(d)/P(s) = .95(.1)/.2) = .475 = 47.5%