MathDB
Painted Cube

Source:

January 7, 2009
geometry3D geometryprobability

Problem Statement

Each face of a cube is painted either red or blue, each with probability 1/2 1/2. The color of each face is determined independently. What is the probability that the painted cube can be placed on a horizontal surface so that the four vertical faces are all the same color? <spanclass=latexbold>(A)</span> 14<spanclass=latexbold>(B)</span> 516<spanclass=latexbold>(C)</span> 38<spanclass=latexbold>(D)</span> 716<spanclass=latexbold>(E)</span> 12 <span class='latex-bold'>(A)</span>\ \frac14 \qquad <span class='latex-bold'>(B)</span>\ \frac{5}{16} \qquad <span class='latex-bold'>(C)</span>\ \frac38 \qquad <span class='latex-bold'>(D)</span>\ \frac{7}{16} \qquad <span class='latex-bold'>(E)</span>\ \frac12