The following question was posed to students at the Harvard Medical 
School: A test for a disease whose prevalence is 1/1000 fails never 
when the person is infected, but has a false positive rate of 5%. A p
erson is picked randomly from the population at large and tests positive. 
What is the probability that this person actually has the disease? 

Assume the false positive rates are purely due to chance (i.e., no 
dependence on conditions of the persons tested). Under the assumptions
stated above, how often needs the test to be repeated, so that we are 
sure with at least 99.9% probability that a person is infected? What 
is then the expected number of tests needed for a sample of 1000 
persons?