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2 answers:
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Answer:
(a) The probability that the new municipal bond issued will receive an A rating given that it was issued by a city is 0.196.
(b) Thus, the probability of municipal bonds issued by suburbs is 0.325.
Step-by-step explanation:
The data provided is as follows:
P (A) = 0.70
P (B) = 0.20
P (C) = 0.10
P (c | A) = 0.50
P (s | A) = 0.40
P (r | A) = 0.10
P (c | B) = 0.60
P (s | B) = 0.20
P (r | B) = 0.20
P (c | C) = 0.90
P (s | C) = 0.05
P (r | C) = 0.05
(a)
The Bayes' theorem states that the conditional probability of an event <em>Y</em> given that another event <em>X</em> has already occurred is:
Compute the probability that the new municipal bond issued will receive an A rating given that it was issued by a city as follows:
Thus, the probability that the new municipal bond issued will receive an A rating given that it was issued by a city is 0.196.
(b)
The law of total probability states that:
Compute the probability of municipal bonds issued by suburbs as follows:
Thus, the probability of municipal bonds issued by suburbs is 0.325.