A bond analyst was given a list of 15 corporate bonds. From that list, she selec

Question

A bond analyst was given a list of 15 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 15 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

Explanation / Answer

N = 15

k = 5

n = 4

P(X = x) = [ kCx ] [ N-kCn-x ] / [ NCn ]

P(X > 2) = 1 - [P(X = 0) + P(X = 1)]

              = 1 - [ [ 5C0 ] [ 10C4-0 ] / [ 15C4 ] + [ 5C1 ] [ 10C3 ] / [ 15C4 ] ]

              = 1 - 0.5934

              = 0.4066

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