Section 7.6 Bayes’ Theorem.

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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 Where Posteriori probability: probability is calculated after the outcomes of the experiment have occurred.

Ex. A store stocks light bulbs from three suppliers 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 So about 0.17