2016 AMC 8 Problem 21
Attempt Problem 21 of the 2016 AMC 8 below, then check your answer against the video solution and professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2016 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
21.
A box contains red chips and green chips. Chips are drawn randomly, one at a time without replacement, until all of the reds are drawn or until both green chips are drawn. What is the probability that the reds are drawn?
Answer: B
Small hint:
The stopping result is determined by which color appears last in the full ordering of the chips.
Big hint:
Count equally likely positions for the two green chips among the five total chip positions.
Video solution:
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Written solution:
The reds are drawn before both green chips exactly when a green chip is the last chip in the full ordering. There are equally likely ways to choose the two positions of the green chips, and of them have a green chip in the last position.
Therefore, the desired probability is
Thus, B is the correct answer.
Problem 21 in other years
- 1985 AMC 8
- 1986 AMC 8
- 1987 AMC 8
- 1988 AMC 8
- 1989 AMC 8
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