Bayes Theorem

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					                 Bayes Theorem
   If the events A1,A2,.......Ak form a partition of sample
 space S, that is the events Ai are mutually exclusive and
their union is S, and if B is any other event of S such that it
     can occur only if one of the Ai occurs then for any i.
                     Bayes Theorem
Q: # In a bolt factory, machines A, B and C manufacture 25, 35 and 40
   percent of the total output respectively. Of their outputs, 5, 4, 2
   percent, respectively are defective bolts. A bolt is selected at random
   and found to be defective. What is the probability that the bolt came
   from machine A? B? C?.
Q:# A manufacturing firm employs three analytical plans for the design
   and development of a particular product. For cost reasons all three
   are used at varying times . In fact plans 1,2 and 3 are used for 30%,
   20% and 50% of the products respectively. The “defect rate “ is
   different for the three procedures as follows
   P(D|p1)=0.01 P(D|P2)=0.03 P(D|P3)=0.02 if a random product was
   observed and found to be defective , which plan was most likely
   used and thus responsible?
Q: # in a college 4 % of men and 1% of women are taller than 6 feet.
   Further more 60% of the students are women. Now if a student is
   selected at random and is taller than 6 feet , then what is the
   probability that the student is a women?

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