4.37 A municipal bond service has three rating categories (A, B, and C). Suppose that in the past year, of the municipal

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4.37 A municipal bond service has three rating categories (A, B,
and C). Suppose 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? 50% is the
probability b. What proportion of municipal bonds are issued by
cities? c. What proportion of municipal bonds are issued by
suburbs?