A bond service has three rating categories (R_1, R_2, and R_3). Suppose that in

Question

A bond service has three rating categories (R_1, R_2, and R_3). Suppose that in the past year, of the bonds issued throughout a country, 60% were rated R_1, 20% were rated R2, and 20% were rated R_3. Out of these bonds, 50% of the R_1 rated bonds were issued by cities, 30% of the R_2 rated bonds were issued by cities, and 80% of the R_3 rated bonds were issued by cities. Use Bayes' Theorem to compute the probability that if a new bond is to be issued by a city, it will receive an R_1 rating. The probability is. (Round to three decimal places as needed.)

Explanation / Answer

Solution:

P(B|A) = P(A|B) . P(B)/P(A)
P(A|city) = P(city|A) . P(A)/P(city)
P(A|city) = 0.3* 0.6/0.48
= 0.375
Percentage of bonds issued to cities is P(city) is.
P(city) = P(city|A) P(A) +P(city|B) P(B) +P(city|C)P(C)

Apart from A, B and C and can be solved by the same method.

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