2. Bayes’ Theorem
Developed by British mathematician Rev. Thomas
Bayes.
The procedure for revising the prior probabilities
based on new information and determining the
probability that a particular effect was due to a
specific cause.
The theorem is based on Conditional probability.
3. Posterior probability
The prior probabilities changed in the light of
new information are called Posterior or Revised
probabilities.
Posterior probabilities are always conditional
probabilities , the conditional event being the
sample information.
Thus a prior probability which is unconditional
becomes a Posterior, which is conditional by
using Bayes’ rule.
4. Continued……..
Posterior probabilities are determined with the
help of Bayes’ theorem:
P(Ai│B) = P(Ai∩B)
P(B)
Where Posterior probability of Ai given B, is the
conditional probability P(Ai│B)
5. Example:
Suppose an item is manufactured by 3 machines X, Y
& Z. All 3 machines have equal capacity & are
operated at the same rate. It is known that the
percentages of defective items produced by X, Y & Z
are 2, 7 and 12 respectively. All the items produced
by X, Y & Z are put into one bin. From this bin, one
item is drawn at random and is found to be
defective. What is the probability that the item was
produced on Y?
