2017 AMC 12A Problem 10
Attempt Problem 10 of the 2017 AMC 12A 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 2017 AMC 12A solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
10.
Chloé chooses a real number uniformly at random from the interval Independently, Laurent chooses a real number uniformly at random from the interval What is the probability that Laurent’s number is greater than Chloé’s number?
Answer: C
Small hint:
Split on whether Laurent’s number is above or below
Big hint:
If it is above he always wins; if below, it is a symmetric coin flip
Solution:
With probability Laurent’s number lies in which exceeds any number Chloé could choose, so he wins for certain.
With the other probability Laurent’s number lies in matching Chloé’s interval; by symmetry he is larger half the time. The total probability is
Thus, the correct answer is C.
Problem 10 in other years
- 1950 AMC 12
- 1951 AMC 12
- 1952 AMC 12
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- 1954 AMC 12
- 1955 AMC 12
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