1. A bond analyst was given a list of 11 corporate bonds. From that list, she se
ID: 3237076 • Letter: 1
Question
1. A bond analyst was given a list of 11 corporate bonds. From that list, she selected 4 whose ratings she felt were in danger of being downgraded in the next year. In actuality, a total of 5 of the 11 bonds on the list had their ratings downgraded in the next year. Suppose that the analyst had simply chosen 4 bonds randomly from this list. What is the probability that at least 2 of the chosen bonds would be among those whose ratings were to be downgraded in the next year?
The probability that at least 2 of the chosen bonds would be downgraded is........
Round to four decimal places as needed
Explanation / Answer
N = 11
k = 5
n = 2
This is hypergeometric distribution
P(X = x) = [ kCx ] [ N-kCn-x ] / [ NCn ]
P(X > 2) = P(X = 2) + P(X = 3) + P(X = 4)
= [ 5C2 ] [ 6C2 ] / [ 11C4 ] + [ 5C3 ] [ 6C1 ] / [ 11C4 ] + [ 5C4 ] [ 6C0 ] / [ 11C4 ]
= 0.6515 (ans)
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