A jar contains exactly 100 marbles; each marble contains

[swerve]

A jar contains exactly 100 marbles; each marble contains exactly 2 colors. Forty-three of the marbles are part-green and 21 of the marbles are part-red. If 3 marbles are to be selected at random, what is the probability that at least 2 of them contain no blue?

1) 61 of the marbles are part-orange.
2) 74 of the marbles are part-yellow.

The OA is C

Source: Princeton Review

[Ian Stewart]

If we have 100 marbles, and each marble is made up of 2 colours, we have 200 colours in total. Using either Statement alone, we haven't accounted for very many of the colours, so we could have quite a few half-blue marbles or we could have none, and our probability of picking half-blue marbles could be nonzero or zero. But using both Statements, we have accounted for 43+21+61+74 = 199 of the 200 colours. So we have either 0 half-blue marbles or 1 half-blue marble. In either case, if we pick two or more marbles, we'll never pick two half-blue marbles, and the probability the question is asking for must be zero.

So the answer is C.