Drawing green, green, then orange

Question

A jar holds 5 green beads and 5 orange beads, 10 in total. You draw 3 beads one at a time, without replacement. What is the probability that the draws come out in the exact order green, green, orange?

Accepted Answer

Order matters, so multiply the chance of each draw in turn, updating the jar as beads leave. First draw green. 5 green out of 10: \frac{5}{10}. Second draw green. One green gone, so 4 green out of 9: \frac{4}{9}. Third draw orange. Two beads gone; all 5 orange still there, out of 8: \frac{5}{8}. Multiply: \frac{5}{10}	imes\frac{4}{9}	imes\frac{5}{8}=\frac{100}{720}=\frac{5}{36}\approx 0.139. Takeaway. Each step uses the counts as they stand at that moment. Beads you have not touched keep their full count, while the color you just drew drops by one.

Drawing green, green, then orange

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