2009 AMC 10B Problems/Problem 25

The following problem is from both the 2009 AMC 12B #17 and 2009 AMC 10B #25, so both problems redirect to this page.

Problem

Each face of a cube is given a single narrow stripe painted from the center of one edge to the center of the opposite edge. The choice of the edge pairing is made at random and independently for each face. What is the probability that there is a continuous stripe encircling the cube?

$\mathrm{(A)}\frac 18\qquad \mathrm{(B)}\frac {3}{16}\qquad \mathrm{(C)}\frac 14\qquad \mathrm{(D)}\frac 38\qquad \mathrm{(E)}\frac 12$

Solution

$\boxed{\frac {3}{16}}$ . The answer is $\mathrm{(B)}$ .

2009 AMC 12B (Problems • Answer Key • Resources)
Preceded by Problem 16	Followed by Problem 18
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All AMC 12 Problems and Solutions

2009 AMC 10B (Problems • Answer Key • Resources)
Preceded by Problem 24	Followed by Last question
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All AMC 10 Problems and Solutions

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2009 AMC 10B Problems/Problem 25

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