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Answer: 62.50%
## 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).
Author: Tanishq Prabhu
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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:
A
62.50%
B
50%
C
80%
D
37.50%