Bayes Theorem (Special Case)
P(F│E) = .
Using Bayes’ Theorem
a. Start a tree diagram with branches representing F1,F2,………….Fn. Label each
branch with its corresponding probability.
b. From the end of each of these branches, draw a branch for event E. Label
this branch with the probability of getting to it, P(E│Fi).
c. You now have n different paths that result in event E. Next to each path,
put its probability—the product of the probabilities that the first branch
occurs,P(Fi) and that the second branch occurs, P(E│Fi)that is, the
product P(Fi)*P(E│Fi)which equals P(Fi ∩ E).
d. P(Fi│E)is found by dividing the probability of the branch for Fi by the
sum of the probabilities of all the branches producing event E.