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