A municipal bond service has three rating categories (A, B, and C). Suppose that of the municipal bonds issued throughout the United States in the past year, 70% were rated A, 20% were rated B, and 10% were rated C. Of the municipal bonds rated A, 5 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? c. What proportion of municipal bonds are issued by suburbs?
A municipal bond service has three rating categories (A, B, and C). Suppose that of the municipal bonds issued throughout the United States in the past year, 70% were rated A, 20% were rated B, and 10% were rated C. Of the municipal bonds rated A, 5 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? c. What proportion of municipal bonds are issued by suburbs?
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A municipal bond service has three rating categories (A, B, and C). Suppose that of the municipal bonds issued throughout
the United States in the past year, 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.
3 a. If a new municipal bond is to be issued by a city, what is the probability that it will receive an A rating?
4 b. What proportion of municipal bonds are issued by cities?
5 c. What proportion of municipal bonds are issued by suburbs?
50%
67%
22%
7
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40%
10%
8 Rating A
9 Rating B
10 Rating C
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50%
20%
60%
20%
20%
10%
90%
5%
5%
200%
65%
35%
4.48
nuBasic Probabilities
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4.48
A municipal bond service has three rating categories (A, B, and C). Suppose that of the municipal bonds issued throughout the
United States in the past year, 70% were rated A, 20% were rated B, and 10% were rated C. Of the municipal bonds rated A, 5
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?
c. What proportion of municipal bonds are issued by suburbs?
4.53
Expert Solution
Step 1
Given:
A rated 70% of 100=70
B rated 20% of 100=20
C rated 20% of 100=20
From A, 50% for cities >>50% of 70=35
From A, 40% for suburbs >>40% of 70=28
From A, 10% for rural >>10% of 70=7
From B, 60% for cities >>60% of 20=12
From B, 20% for suburbs >>20% of 20=4
From B, 20% for rural >>20% of 20=4
From C, 90% for cities >>90% of 10=9
From C, 5% for suburbs >>5% of 10=0.5
From C, 5% for rural >>5% of 10=0.5
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