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Bead Probability

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January 9, 2009
probability

Problem Statement

A bag contains two red beads and two green beads. You reach into the bag and pull out a bead, replacing it with a red bead regardless of the color you pulled out. What is the probability that all beads in the bag are red after three such replacements? <spanclass=′latex−bold′>(A)</span> 18<spanclass=′latex−bold′>(B)</span> 532<spanclass=′latex−bold′>(C)</span> 932<spanclass=′latex−bold′>(D)</span> 38<spanclass=′latex−bold′>(E)</span> 716 <span class='latex-bold'>(A)</span>\ \frac{1}{8} \qquad <span class='latex-bold'>(B)</span>\ \frac{5}{32} \qquad <span class='latex-bold'>(C)</span>\ \frac{9}{32} \qquad <span class='latex-bold'>(D)</span>\ \frac{3}{8} \qquad <span class='latex-bold'>(E)</span>\ \frac{7}{16}
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