Example

A patient takes a lab test and the result comes back positive. The test returns a correct positive result in only $98%$ of the cases in which the disease is actually present, and a correct negative result in only $97%$ of the cases in which the disease is not present. Furthermore, $.008$ of the entire population have this cancer. \[ \array{ P(cancer) = .008 & P(\neg cancer) = .992 \\ P(\oplus \,|\, cancer) = .98 & P(\ominus \,|\, cancer) = .02 \\ P(\oplus \,|\, \neg cancer) = .03 & P(\ominus \,|\, \neg cancer) = .97} \]
If a new patient comes in with a positive test result, whats the probability that he has cancer? \[ \array{ P(\oplus\,|\,cancer) P(cancer) = (.98).008 = .0078 \\ P(\oplus\,|\,\neg cancer) P(\neg cancer) = (.03).992 = .0298 } \] so $h_{MAP} = \neg cancer$.