Stochastic Modelling for Systems Biology, Second Edition, 2nd Edition

PROBA BILITY 61

Example

A clinic offers you a free test for a very rare, but hideous disease. The test they offer

is very reliable. If you have the disease it has a 98% chance o f giving a positive

result, and if you do not have the disease, it has only a 1% chance of g iving a positive

result. Desp ite having no a priori reason to suppose that you have the disease, you

nevertheless decide to take the test and find that y ou te st positive — what is the

probability that you have the disease?

Let P be the event “test positive” a nd D be the event “you have the disease”. We

know that

P(P |D) = 0.98 and that P(P |D

c

) = 0.01.

We want to k now P(D|P ), so