
Explanation:
Since the defaults are independent events with a constant probability, the number of defaults follows a binomial distribution. Using the binomial probability formula:
Where:
(number of bonds)
(number of defaulting bonds)
(probability of default)
$1-p = 0.90$ (probability of non-default)
.
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Q.69 A portfolio consists of three bonds and each bond has a 1-year default probability of 10%. The event of default for each of the bonds is independent. What is the probability of exactly one bond defaulting over the next year?
A
0.243
B
0.1215
C
0.027
D
0.757