Question:

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 US, 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.

1. If a new municipal bond is to be issued by a city, what is the probability that it will receive an A rating?
2. What proportion of municipal bonds is issued by cities?
3. What proportion of municipal bonds is issued by suburbs?

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