2010 AMC 12B Problems/Problem 18

Problem 18

A frog makes $3$ jumps, each exactly $1$ meter long. The directions of the jumps are chosen independenly at random. What is the probability that the frog's final position is no more than $1$ meter from its starting position?

$\textbf{(A)}\ \dfrac{1}{6} \qquad \textbf{(B)}\ \dfrac{1}{5} \qquad \textbf{(C)}\ \dfrac{1}{4} \qquad \textbf{(D)}\ \dfrac{1}{3} \qquad \textbf{(E)}\ \dfrac{1}{2}$

Solution

2010 AMC 12B (Problems • Answer Key • Resources)
Preceded by Problem 17	Followed by Problem 19
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2010 AMC 12B Problems/Problem 18

Problem 18

Solution

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