A municipal bond service has three rating categories(A B and C). Sup- pose that

Question

A municipal bond service has three rating categories(A B and C). Sup- pose that in the past year, of the municipal bonds issued throughout the United States, 70% were rated A, 20% were rated B, and 10% were rated C. Of the municipal bonds rated A, 50% were issued by cities, 40% by suburbs, and 10% by rural areas. Of the municipal bonds rated B, 60% were issued by cities, 20% by suburbs, and 20% by rural areas. Of the municipal bonds rated C, 90% were issued by cities, 5% by suburbs, and 5% by rural areas. (a)If a new municipal bond is to be issued by a city, what is the probability that it will receive an A rating? (b)What proportion of municipal bonds are issued by cities?

Explanation / Answer

a) P(A rating | municipal bond is issued in city) = P(A rating and municipal bond is issued in a city)/ P(municipal bond is issued in a city)

= 0.7x0.5 / (0.7x0.5 + 0.2x0.6 + 0.1x0.9)

= 0.35/0.56

= 0.625

b) Proportion of municipal bonds issued by cities = 0.7x0.5 + 0.2x0.6 + 0.1x0.9 = 0.56

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