11-25-2014, 03:00 PM
Bayes’ formula is useful for calculating conditional probabilities.
If we set
p(E) = A = .001 as the probability of a member of the population having a certain illness E,
p(F|E) = B = .99 as the probability of a positive result for the illness test F if the member has the illness E,
p(F|-E) = C = .05 as the probability of a positive result for the illness test F if the member does NOT have the illness E, a so-called false positive,
then the formula
D = A * B / ( A * B + ( 1 – A) * C )
can be used to calculate
p(E|F) = D
ie the probability of having the illness E if the test F is positive, which for the given data is .019
If we set
p(E) = A = .001 as the probability of a member of the population having a certain illness E,
p(F|E) = B = .99 as the probability of a positive result for the illness test F if the member has the illness E,
p(F|-E) = C = .05 as the probability of a positive result for the illness test F if the member does NOT have the illness E, a so-called false positive,
then the formula
D = A * B / ( A * B + ( 1 – A) * C )
can be used to calculate
p(E|F) = D
ie the probability of having the illness E if the test F is positive, which for the given data is .019