Five companies (A, B, C, D, and E) that make elec- trical relays compete each year to be the sole sup- plier of relays to a major automobile manufacturer. The auto company’s records show that the probabili- ties of choosing a company to be the sole supplier are Supplier chosen: A B C D E Probability: .20 .25 .15 .30 .10 a. Suppose that supplier E goes out of business this year, leaving the remaining four companies to compete with one another. What are the new probabilities of companies A, B, C, and D being chosen as the sole supplier this year? b. Suppose the auto company narrows the choice of suppliers to companies A and C. What is the probability that company A is chosen this year?

a

b

Step-by-step explanation:

From the question we are told that

   The probabilities are

Supplier  chosen            A                     B                    C            

Probability                P(a) = 0.20       P(b) =  0.25   P(c) =  0.15      

                                       D                      E

                                P(d) =  0.30     P(e) = 0.10

Generally the new probability of companies A being chosen as the sole supplier this year given that supplier E goes out of business is mathematically represented as below according to Bayes theorem

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Generally the new probability of companies B  being chosen as the sole supplier this year given that supplier E goes out of business is mathematically represented as below according to Bayes theorem

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Generally the new probability of companies C  being chosen as the sole supplier this year given that supplier E goes out of business is mathematically represented as below according to Bayes theorem

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Generally the new probability of companies D  being chosen as the sole supplier this year given that supplier E goes out of business is mathematically represented as below according to Bayes theorem

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Generally the probability that  B, D , E  are not chosen this year is mathematically represented as

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Generally the probability that A is chosen given that E , D , B  are rejected this year is mathematically represented  as

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