1983 AMC 12 Problem 26
Attempt Problem 26 of the 1983 AMC 12 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 1983 AMC 12 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
26.
The probability that event occurs is the probability that event occurs is Let be the probability that both and occur. The smallest interval necessarily containing is the interval
Answer: D
Small hint:
Apply inclusion-exclusion to events and
Big hint:
Bound between and
Solution:
Inclusion-exclusion gives Since it follows that Both endpoints can occur, so this is the smallest necessary interval.
Therefore, the correct answer is D.
Problem 26 in other years
- 1950 AMC 12
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