2000 AMC 8 Problem 21
Attempt Problem 21 of the 2000 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 2000 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
21.
Keiko tosses one penny and Ephraim tosses two pennies. The probability that Ephraim gets the same number of heads that Keiko gets is
Answer: B
Small hint:
List Keiko’s result and Ephraim’s two-coin result
Big hint:
Count matching head totals among the equally likely outcomes
Solution:
There are equally likely outcomes if we record Keiko’s coin and Ephraim’s two coins.
If Keiko gets heads, Ephraim must get exactly one head; this happens in outcomes. If Keiko gets tails, Ephraim must get no heads; this happens in outcome.
So of the equally likely outcomes work, and the probability is
Thus, B is the correct answer.
Problem 21 in other years
- 1985 AMC 8
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