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, 70​% were rated R 1​, 20​% were rated R 2​, and 10​% were rated R 3. Out of these​ bonds, 40​% of the R 1 rated bonds were issued by​ cities,50​% 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 R1 rating.

Answer 1

We have ,

P( R1 ) = 70% = 0.7

P( R2 ) = 20% = 0.2

P( R3) = 10% = 0.1

Let , C be the event that bonds were issued by cities.

40​% of the R1 rated bonds were issued by​ cities

P( C | R1 ) = 0.4

50​% of the R2 rated bonds were issued by​ cities

P( C | R2 ) = 0.5

80​% of the R3 rated bonds were issued by cities

P( C | R3 ) = 0.8

We have to find probability that if a new bond is to be issued by a​ city, it will receive an R1 rating.

i. e we have to find P( R1 | C )

Using Bayes' Theorem.

Probability that if a new bond is to be issued by a​ city, it will receive an R1 rating is 0.6087