Yellow, then purple, then purple

Question

A bag holds 6 yellow tiles and 4 purple tiles, 10 in total. You draw 3 tiles one at a time, without replacement.

What is the probability that the draws come out in the exact order yellow, purple, purple?

Accepted Answer

Order matters, so multiply the draw-by-draw chances, shrinking the bag each time. First draw yellow. 6 yellow out of 10: \frac{6}{10}. Second draw purple. One yellow gone; 4 purple still there, out of 9: \frac{4}{9}. Third draw purple. One purple now gone, so 3 purple out of 8: \frac{3}{8}. Multiply: \frac{6}{10}	imes\frac{4}{9}	imes\frac{3}{8}=\frac{72}{720}=\frac{1}{10}=0.1. Takeaway. Track the color you need at each position and use the current counts. The purples deplete across the two later draws, which is why the last factor drops from 4/9 to 3/8.

Yellow, then purple, then purple

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