The basket contains:
- Red marbles: 4
- Blue marbles: 5
- Green marbles: 3
Total marbles = 4 + 5 + 3 = 12
For "at least one blue" problems, use the complement:
P(at least one blue) = 1 - P(no blue marbles)
Total ways to pick 3 marbles from 12:
C(12,3)=3×2×112×11×10
=61320
=220
Ways to pick 3 marbles with no blue (only red and green):
Non-blue marbles = 4 + 3 = 7
C(7,3)=3×2×17×6×5
=6210
=35
P(no blue marbles) = 22035=447
P(at least one blue) = 1−447
=4444−447
=4437
Therefore, the probability that at least one marble is blue is 4437.