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Five randomly picking chips

Source: 2001 AMC-12 #11

December 3, 2005
probabilitycomplementary countingAMC

Problem Statement

A box contains exactly five chips, three red and two white. Chips are randomly removed one at a time without replacement until all the red chips are drawn or all the white chips are drawn. What is the probability that the last chip drawn is white? <spanclass=′latex−bold′>(A)</span> 310<spanclass=′latex−bold′>(B)</span> 25<spanclass=′latex−bold′>(C)</span> 12<spanclass=′latex−bold′>(D)</span> 35<spanclass=′latex−bold′>(E)</span> 710 \displaystyle <span class='latex-bold'>(A)</span> \ \frac {3}{10} \qquad <span class='latex-bold'>(B)</span> \ \frac {2}{5} \qquad <span class='latex-bold'>(C)</span> \ \frac {1}{2} \qquad <span class='latex-bold'>(D)</span> \ \frac {3}{5} \qquad <span class='latex-bold'>(E)</span> \ \frac {7}{10}
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