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Counted the favorable outcomes for each color separately: C(3,3) for green, C(4,3) for red, C(2,3) for blue (which is zero).
Break the problem into mutually exclusive cases: all green, all red, or all blue. Compute the probability for each case using combinations or sequential probabilities, then sum them since the events are disjoint.
Pro tip: State your assumptions clearly (e.g., 'assuming each cube is equally likely to be drawn') and mention that you're using combinations because order doesn't matter. This shows attention to detail and mathematical rigor.
Identify that we need the probability of drawing three cubes of the same color from a bag with 3 green, 4 red, and 2 blue cubes, without replacement.
Recognize that the only possible monochromatic draws are all green, all red, or all blue. These events are mutually exclusive.
Compute the total number of ways to draw 3 cubes from 9 using combinations: C(9,3) = 84.
For each color, compute the number of ways to draw 3 cubes of that color: green: C(3,3)=1, red: C(4,3)=4, blue: C(2,3)=0 (impossible).
Add the favorable outcomes: 1+4+0=5. Then divide by total outcomes: 5/84 ≈ 0.0595 or about 5.95%.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.