1995 AMC 8 Problem 20
Attempt Problem 20 of the 1995 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 1995 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
20.
Diana and Apollo each roll a standard die obtaining a number at random from to What is the probability that Diana’s number is larger than Apollo’s number?
Answer: B
Small hint:
Of the equally likely outcomes, some are ties; remove those
Big hint:
By symmetry, Diana is larger in exactly half of the non-tie outcomes
Solution:
There are equally likely outcomes, of which are ties, leaving outcomes with different numbers.
By symmetry, Diana is larger in exactly half of those, or so the probability is
Thus, the correct answer is B .
Problem 20 in other years
- 1985 AMC 8
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