bond service has three rating (A, B, and C). Suppose that in the past year, of t
ID: 3074086 • Letter: B
Question
bond service has three rating (A, B, and C). Suppose that in the past year, of the municipal bonds issued thoughout a country, 70% were rated A, 10% were rated B, and 20% were rated C. ofthe municipal bonds rated A, 40% were issued by otes, 40% by suburbs, and 20% by rural areas. Ofthe municipal bonds rated B, 60% were issued by dies, 10% by suburbs, and 30% by rural areas. Of the municpal bonds rated C 90% wore issued by cies, 5% by s buts, and 5% by rural areas. Complete (a) through c) below a. If a new municipal bond is to be issued by a city, what is the probability that it will receive an A rating? 0.538 (Round to three decimal places as needed.) b. What proportion of municipal bonds are issued by cities? Round to three decimal places as needed )Explanation / Answer
a) P(issued by city) = P(issued by city | rating A) * P(rating A) + P(issued by city | rating B) * P(rating B) + P(issued by city | rating C) * P(rating C)
= (0.4*0.7) + (0.6*0.1) + (0.9*0.2)
= 0.52
If a new municipal bond is to be issued by a city, the probability that it will receive an A rating
= P(A rating | issued by city)
= P(issued by city | rating A) * P(rating A) / P(issued by city)
= (0.4*0.7) / 0.52
= 0.28/0.52
= 0.538462
b) The proportion of municipal bonds that are issued by cities
= P(issued by city | rating A) * P(rating A) + P(issued by city | rating B) * P(rating B) + P(issued by city | rating C) * P(rating C)
= (0.4*0.7) + (0.6*0.1) + (0.9*0.2)
= 0.52
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