Financial Risk Manager Part 1
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The probabilities that Bond A and Bond X will default in the next two years are 10% and 8%, respectively. The probability that both bonds will default simultaneously in the next two years is 5%. The probability that Bond A will default given that Bond X has already defaulted is closest to:
Other
Community
NNikitesh
A
62.50%
B
50%
C
80%
D
37.50%
Explanation:
Explanation
This is a conditional probability problem. We are given:
- P(A) = Probability that Bond A defaults = 10% = 0.10
- P(X) = Probability that Bond X defaults = 8% = 0.08
- P(A ∩ X) = Probability that both bonds default = 5% = 0.05
We need to find P(A|X) = Probability that Bond A defaults given that Bond X has already defaulted.
Using the formula for conditional probability:
Substituting the values:
Therefore, the probability that Bond A will default given that Bond X has already defaulted is 62.50%.
Key Concepts:
- Conditional probability formula: P(A|B) = P(A ∩ B)/P(B)
- This measures the probability of event A occurring given that event B has already occurred
- The intersection probability (both events occurring) is divided by the probability of the conditioning event
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