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 throughout the United States, 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 issued 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.

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

What proportion of municipal bonds are issued by cities?

What proportion of municipal bonds are issued by suburbs?

Explanation / Answer

ans

a)

from given data

.7 * .5 = .35 of all bonds are A cities
.7 * .4 = .28 of all bonds are A suburbs
.7 * .1 = .07 of all bonds are A rural
.2 * .6 = .12 of all bonds are B cities
.2 * .2 = .04 of all bonds are B suburbs
.2 * .2 = .04 of all bonds are B rural
.1 * .9 = .09 of all bonds are C cities
.1 * .05 = .005 of all bonds are C suburb
.1 * .05 = .005 of all bonds are C rural

.28 / (.28 + .04 + .005)
.28 / .325
.8615
86.15% of suburban bonds have an A rating

b)

.35 / (.35 + .28 + .07)
.35 / .7
.5
50% of all A bonds are city

c)

.28 + .04 + .005 =
.325
32.5% of all bonds are issued by suburbs

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