A municipal bond service has three rating categories (A, B, and C). Suppose that

Question

A municipal bond service has three rating categories (A, B, and C). Suppose that in the past year, of the municipal bonds issued thoughout a country, 60% were rated A, 10% were rated B, and 30% were rated C. Of the municipal bonds rated A, 50% were issued by cities, 10% by suburbs, and 40% by rural areas. Of the municipal bonds rated B, 40% were issued by cities, 50% by suburbs, and 10% by rural areas. Of the municipal bonds rated C, 80% were issued by cities, 15% by suburbs, 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? (Round to three decimal places as needed.)

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

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

Explanation / Answer

Ans:

b)P(cities)=P(cities/A)*P(A)+P(cities/B)*P(B)+P(cities/C)*P(C)

=0.5*0.6+0.4*0.1+0.8*0.3

=0.58

c)P(suburbs)=P(suburbs/A)*P(A)+P(suburbs/B)*P(B)+P(suburbs/C)*P(C)

=0.1*0.6+0.5*0.1+0.15*0.3=0.155

a)P(A/cities)=P(cities/A)*P(A)/P(cities)=0.5*0.6/0.58=0.3/0.58=0.517

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.