A bond analyst was given a list of twelve corporate bonds. From that list, she selected three whose ratings she felt were in danger of being downgraded in the next year. In actuality, total of four of the twelve bonds on the list had their ratings downgraded in the next year. Suppose that the analyst had simply chosen three bonds randomly from this list. What is the probability that at least two of the chosen bonds would be among those whose ratings were to be downgraded in the next year?
I got an answer of .2364 but not sure if I did it right.
I did 1-( (9choose4+3*9choose3)/(12choose4))