swerve wrote: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.

To calculate the probability of picking at least 2 marbles that contain no blue, we need to know how many of the 100 marbles are part-blue.
Question stem, rephrased:
How many of the 100 marbles are part-blue?

Total marbles = (total part-green) + (total part-red) + (total part-orange) + (total part-yellow) + (total part-blue) - (number of marbles that contain exactly two colors).

Total marbles = 100.
Total part-green = 43.
Total part-red = 21.
Since all of the marbles contain exactly 2 colors, the number of marbles that contain exactly two colors = 100.

Plugging these values into the equation above, we get:
100 = 43 + 21 + (total part-orange) + (total part-yellow) + (total part-blue) - 100
200 = 64 + (total part-orange) + (total part-yellow) + (total part-blue)
136 - (total part-orange) - (total part-yellow) = total part-blue
Total part-blue = 136 - (total part-orange) - (total part-yellow).

Statement 1: total part-orange = 61
Plugging this value into the blue equation above, we get:
Total part-blue = 136 - 61 - (total part-yellow).
Since the value in red is unknown, the number of part-blue marbles cannot be determined.
INSUFFICIENT.

Statement 2: total part-yellow = 74
Plugging this value into the blue equation above, we get:
Total part-blue = 136 - (total part-orange) - 74.
Since the value in red is unknown, the number of part-blue marbles cannot be determined.
INSUFFICIENT.

Statements combined: total part-orange = 61 and total part-yellow = 74
Plugging these values into the blue equation above, we get:
Total part-blue = 136 - 61 - 74 = 1.
SUFFICIENT.

The correct answer is C.