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# PROBABILITY

DOI link for PROBABILITY

PROBABILITY book

# PROBABILITY

DOI link for PROBABILITY

PROBABILITY book

## ABSTRACT

To illustrate this formula, let us take a factory that has 3 machines for the production of bolts, of which it produces 60,000 pieces daily. Of these, 10,000 are produced by machine A

1 , 20,000 by machine A2, and 30,000 by machine A3. All three machines

occasionally produce faulty pieces, F. On average, the rejection rates of the 3 machines are as follows: 4 percent in the case of A

1 , 2 percent in the case of A2, 4

percent in the case of A 3 . Given a defective bolt taken from the rejects, we ask for the

probability that it was produced by each of the three machines. In order to calculate such a probability by means of Bayes’s rule, we start from prior probabilities, obtained in this case from the information concerning the production of the machines. They are as follows:

P(A 1 ) 5 10,000/60,000 5 1/6

P(A2) 5 20,000/60,000 5 1/3 P(A

3 ) 5 30,000/60,000 5 1/2.