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06 Oct 2017, 06:12
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
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CHALLENGE QUESTIONS
Bonds rated B have a 25% chance of default in five years. Bonds rated C have a 40% chance of default in 5 years. A portfolio consists of 30% B-rated bonds and 70% of C-rated bonds. If a randomly selected bond defaults in a five year period, what is the probability that it was a B-rated bond?
A. 3/40
B. 15/71
C. 1/4
D. 3/10
E. 56/71
06 Oct 2017, 06:29
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Bunuel
CHALLENGE QUESTIONS
Bonds rated B have a 25% chance of default in five years. Bonds rated C have a 40% chance of default in 5 years. A portfolio consists of 30% B-rated bonds and 70% of C-rated bonds. If a randomly selected bond defaults in a five year period, what is the probability that it was a B-rated bond?
A. 3/40
B. 15/71
C. 1/4
D. 3/10
E. 56/71
hi..
In such Qs we have to note that the EVENT has already happened
so first find the ways in which it can happen..
let the total bonds be 100 - 30 B rated and 70 C- rated
1) B rated bonds -
25 % chances and total 30 of them so \(\frac{25}{100}*30=\frac{15}{2}\)
2) C-rated bonds -
40% chances and total 70 of them so \(\frac{40}{100}*70=28\)
so total = \(\frac{15}{2}+28\)
now let's find the prob it is B-rated
= \(\frac{15}{2}/(\frac{15}{2}+28)=\frac{15}{15+56}=\frac{15}{71}\)
ans B
06 Oct 2017, 06:52
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This sum can be solved using Bayes' Theorem
Lets point out different events.
The event that bond B is selected is say A1.
hence P(A1)= 3/10
The event that bond C is selected is say A2.
hence P(A2)= 7/10
let D be the event that default is selected in five years.
probability of default in bond B= P(D/A1) = 25%= 1/4
probability of default in bond c= P(D/A2) = 40%= 2/5
Now we are asked to find probability of choosing bond B when default is already selected.
i.e. P(A1/D)=?
According to Bayes's Theorem,
P(A1/D)= P(A1)*P(D/A1) / { P(A1)*P(D/A1) + P(A2)*P(D/A2) }
P(A1/D)= 3/10 *(1/4) / { 3/10 *(1/4) + 7/10*(2/5) }
after simplifying above equation ,
P(A1/D) = 15/71
Answer is option B.
Hope it is a correct approach.
Kudos if it helps.
Lets point out different events.
The event that bond B is selected is say A1.
hence P(A1)= 3/10
The event that bond C is selected is say A2.
hence P(A2)= 7/10
let D be the event that default is selected in five years.
probability of default in bond B= P(D/A1) = 25%= 1/4
probability of default in bond c= P(D/A2) = 40%= 2/5
Now we are asked to find probability of choosing bond B when default is already selected.
i.e. P(A1/D)=?
According to Bayes's Theorem,
P(A1/D)= P(A1)*P(D/A1) / { P(A1)*P(D/A1) + P(A2)*P(D/A2) }
P(A1/D)= 3/10 *(1/4) / { 3/10 *(1/4) + 7/10*(2/5) }
after simplifying above equation ,
P(A1/D) = 15/71
Answer is option B.
Hope it is a correct approach.
Kudos if it helps.
