Homework: HW. 4.3 Score: 0 of 1 pt 4.3.37 3013(2complete) Hw Score: 66.67%, 2 of

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Homework: HW. 4.3 Score: 0 of 1 pt 4.3.37 3013(2complete) Hw Score: 66.67%, 2 of 3 pts Question Help * Amniopai bond service has tree ratng categories (A B, and C). Suppose that n the past year ofthe muripal bonds issued thoughout acounry, 50% were rated A,40% were rated B and 10% were rated C Ofthe murepal bonds rated A 60% were asued by otna 30% by souta and 10% by neal seas one muopa bonds rated B. T0% were issued by cities, 10% by subuts, and 20% by nral areas Ofte municipal bonds rated C. 90% were issued by aties, 5% by burbs, and S% by rural areas. Complete (a) trough (c) below. anew municipal bond is to beissued by aoty, what sthe probabity hat twa 448 (Round to three decimal places as needed ) b. What proportion of municipal bonds are issued by cities? (Round to tree-places as needed) a. e an A rating? Enter your answer in the answer box and then click Check Answer Clear All Check Anwer 20 p 5 command option

Explanation / Answer

From the given information we have

P(A) = 0.50, P(B) = 0.40, P(C) =0.10

And

P(city|A) = 0.60

P(city|B) = 0.70

P(city|C) = 0.90

(a)

By the Baye's theorem, the required probability is

P(A|city) = [P(city |A)P(A) ] / [P(city |A)P(A)+P(city |B)P(B)+P(city |C)P(C) ] = [0.60*0.50] / [0.60*0.50 + 0.70*0.40 + 0.90*0.10 ]= 0.3 / 0.67 = 0.4478

Answer: 0.448

(b)

By the law of total probability, the requried probability is

P(city) = P(city |A)P(A)+P(city |B)P(B)+P(city |C)P(C) = 0.67

Answer: 0.670

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