Difference between revisions of "2010 AMC 12B Problems/Problem 18"

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== Problem 18 ==
 
== Problem 18 ==
 
A frog makes <math>3</math> jumps, each exactly <math>1</math> 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 <math>1</math> meter from its starting position?
 
A frog makes <math>3</math> jumps, each exactly <math>1</math> 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 <math>1</math> meter from its starting position?

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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

See also

2010 AMC 12B (ProblemsAnswer KeyResources)
Preceded by
Problem 17
Followed by
Problem 19
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
All AMC 12 Problems and Solutions