Statistics

[huy.duong@ctsu.ox.ac.uk]

>	A blood test is 95 percent effective in detecting a certain
>disease when it is, in fact, present. However, the test also yields a 
>"false positive" result for 1 percent of the healthy persons tested.
>(That is if a healthy persion is tested, then , with probability .01,
>the test result will imply he or she has the desease.) If .5 percent
>of the population actually has the disease, what is the probability a person 
>has the desease given that the test result is positive ?

95.5% of the population are healthy; 0.5% of the population are ill.
A positive result can come from

1) the 95.5% who are healthy when the test wrongly diagnoses 1% of them
to be ill, which is 95.5%*1%=0.955% of the population,

or

2) the 0.5% who are ill when the test correctly diagnoses 95% them to be
ill, which is  0.5%*95%=0.475% of the population.

So a person diagnosed to be ill has a ~1/3 chance of having come from
the ill population.

Huy