Download Section 7.6

Section 7.6
Bayes’ Theorem
Bayes’ Theorem
Let A1, A2, …, An be a partition of a sample space S and
let E be an event of the experiment such that P(E) is not
zero. Then the posteriori probability P(Ai|E) is given
by
P  Ai | E  
P  Ai  P  E | Ai 
P  A1  P  E | A1   P  A2  P  E | A2   ...  P  An  P  E | An 
Where 1  i  n
Posteriori probability: probability is calculated after the
outcomes of the experiment have occurred.
Ex. A store stocks light bulbs from three suppliers.
Suppliers A, B, and C supply 10%, 20%, and 70% of the
bulbs respectively. It has been determined that
company A’s bulbs are 1% defective while company B’s
are 3% defective and company C’s are 4% defective. If
a bulb is selected at random and found to be defective,
what is the probability that it came from supplier B?
Let D = defective
P  B | D 

P  B P  D | B
P  A P  D | A  P  B  P  D | B   P C  P  D | C 
0.2  0.03
0.1 0.01  0.2  0.03  0.7  0.04 
So about 0.17
 0.1714