1987 AMC 8 Problem 25
Attempt Problem 25 of the 1987 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 1987 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
25.
Ten balls numbered to are in a jar. Jack reaches into the jar and randomly removes one of the balls. Then Jill reaches into the jar and randomly removes a different ball. What is the probability that the sum of the two numbers on the balls removed is even?
Answer: A
Small hint:
The sum of two numbers is even exactly when both are odd or both are even
Big hint:
There are odd and even balls; count the matching-parity pairs out of all pairs
Solution:
The sum is even when both balls are odd or both are even. There are all-odd pairs and all-even pairs, for favorable pairs.
The total number of pairs is so the probability is
Thus, the correct answer is A .
Problem 25 in other years
- 1985 AMC 8
- 1986 AMC 8
- 1988 AMC 8
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- 1990 AMC 8
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- 1992 AMC 8
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