1986 AMC 8 Problem 24
Attempt Problem 24 of the 1986 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 1986 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
24.
The students at King Middle School are divided into three groups of equal size for lunch. Each group has lunch at a different time. A computer randomly assigns each student to one of the three lunch groups. The probability that three friends, Al, Bob, and Carol, will be assigned to the same lunch group is approximately
Answer: B
Small hint:
Fix Al’s group; then find the chance that Bob lands in that same group
Big hint:
After Al’s group is fixed, Bob’s chance is and then Carol’s is
Solution:
Whatever group Al is in, Bob joins that same group with probability If Bob does, Carol joins them with probability
Thus all three share a group with probability closest to
Thus, the correct answer is B .
Problem 24 in other years
- 1985 AMC 8
- 1987 AMC 8
- 1988 AMC 8
- 1989 AMC 8
- 1990 AMC 8
- 1991 AMC 8
- 1992 AMC 8
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