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% were issues by suburbs, and 10% were issued by rural areas.

• OF the municipal bonds rated B, 60% were issued by cities, 20% were issued by suburbs, and 20% were issued by rural areas.

• Of the municipal bonds rated C, 90% were issued by cities, 5% were issued by suburbs, and 5% were issued by rural areas.

1. If a new municipal bond is to be issued by a city, what is the probability that it will receive an A rating?
   1. 35%
   2. 50%
   3. 28%
   4. 62.5%
   5. 12%

Answer 1

Desired Probability,

$P(A \ rating | issued \ by \ city) = \frac{P(A \ rating \cap issued \ by \ city) }{P(issued \ by \ city)} = \frac{0.7 * 0.5}{0.7 * 0.5 + 0.2 * 0.6 + 0.1 * 0.9}$

So, $P(A \ rating | issued \ by \ city) = 0.625 \approx 62.5\%$

Option D is correct.

**If the answer does not match please comment.