Please answer a,b,c. Thanks! were issued by cities, 40% by suburbs, and 10% by r

Question

Please answer a,b,c. Thanks!

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 rnu nicipal 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 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% probability that it will receive an A rating? b. W hat proportion of municipal bonds are issued by cities? c. What proportion of municipal bonds are issued by suburbs?

Explanation / Answer

a)) If a new municipal bond is to be issued by a city, what is the probability it will receive an A rating?

It is given that: P(A) = 0.70

                         P(B) = 0.20

                         P(C) = 0.10.

We have to find the probability of getting rating A if a new bond is issued by the city:

P(A/city) = P(A int city)/P(city)

               = 0.50*0.70/0.625

              = 0.625

b)) What proportion of municipal bonds are issued by cities?

      P(city) = 0.56

c)) What proportion of municipal bonds are issued by suburbs?

  P(suburbs)= 0.325

Ratings Issuer A B C Total City 0.50*0.70 = 0.35 0.60*0.20 = 0.12 0.90*0.10 = 0.09 0.35 + 0.12 + 0.09 = 0.56 Suburbs 0.40*0.70 = 0.28 0.20*0.20 = 0.04 0.05*0.10 = 0.005 0.28 + 0.04 + 0.005 = 0.325 Rural 0.10*0.70 = 0.07 0.20*0.20 = 0.04 0.05*0.10 = 0.005 0.07 + 0.04 + 0.005 = 0.115 Total 0.7 0.2 0.1

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