2002 AMC 8 Problem 12

Attempt Problem 12 of the 2002 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 2002 AMC 8 solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

12.

A board game spinner is divided into three regions labeled A,A, BB and C.C. The probability of the arrow stopping on region AA is 13\frac{1}{3} and on region BB is 12.\frac{1}{2}. The probability of the arrow stopping on region CC is
112\dfrac{1}{12}
16\dfrac{1}{6}
15\dfrac{1}{5}
13\dfrac{1}{3}
25\dfrac{2}{5}
Answer: B
Concepts:basic probabilitycomplementary probability
Small hint:
The probabilities of A,A, B,B, and CC add to 1.1.
Big hint:
Subtract the probabilities for AA and BB from 1.1.
Solution:
The total probability is 1.1. We need to subtract the probability of the spinner landing on BB and AA to get C,C, which is 1−13−12=16. 1 - \dfrac{1}{3} - \dfrac{1}{2} = \dfrac{1}{6}.
Thus, B is the correct answer.
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