Posts Tagged ‘Bayes Theorem’

Bayes Theorem (Special Case)

Bayes Theorem (Special Case)

P(F│E) = \frac{P(F)\cdot P(E\mid F)}{P(F)\cdot P(E\mid F)+P({F}')\cdot P(E\mid {F}')}.

 

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.