2011 AMC 8 Problem 12
Attempt Problem 12 of the 2011 AMC 8 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2011 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
12.
Angie, Bridget, Carlos, and Diego are seated at random around a square table, one person to a side. What is the probability that Angie and Carlos are seated opposite each other?
Answer: B
Small hint:
Carlos has three possible seats, only one opposite Angie.
Big hint:
Fix Angie in one seat by symmetry.
Solution:
Consider that Angie’s seat is chosen. Carlos has an equal probability of being in any of the other seats. Only one of them is opposite Angie, however. Therefore, the probability is
Thus, B is the correct answer.
Problem 12 in other years
- 1985 AMC 8
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