Drawing red, then blue, then red

Question

A cup holds 6 red chips and 4 blue chips, 10 in total. You draw 3 chips one at a time, without putting any back.

What is the probability that the draws come out in the exact order red, then blue, then red?

Accepted Answer

Here order matters, so we track each draw in turn and multiply the chances, shrinking the cup after each pull. First draw red. 6 red out of 10: \frac{6}{10}. Second draw blue. One red is gone, so 4 blue remain out of 9 chips: \frac{4}{9}. Third draw red. Now one red and one blue are gone; 5 red remain out of 8 chips: \frac{5}{8}. Multiply the three stages, since we need this specific order: \frac{6}{10}	imes\frac{4}{9}	imes\frac{5}{8}=\frac{120}{720}=\frac{1}{6}\approx 0.167. Takeaway. For a specific ordered sequence, multiply the draw-by-draw chances, updating the counts after each pull. O…

Drawing red, then blue, then red

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