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:
Explanation:
Explanation
This question involves conditional probability calculation. Given:
- P(A) = Probability of Bond A default = 10%
- P(X) = Probability of Bond X default = 8%
- P(A ∩ X) = Probability of both bonds defaulting = 5%
Using the conditional probability formula: [ P(A|X) = \frac{P(A \cap X)}{P(X)} ]
Substituting the values: [ P(A|X) = \frac{5%}{8%} = \frac{5}{8} = 0.625 = 62.5% ]
Therefore, the probability that Bond A will default given that Bond X has already defaulted is 62.50%.
Key Concept: Conditional probability measures the probability of an event occurring given that another event has already occurred. The formula is P(A|B) = P(A∩B)/P(B).