MathDB
Probability Cheryl Draws Double

Source: 2015 AMC 12A #9

February 4, 2015
probabilitySupportAMC 10AMC

Problem Statement

A box contains 22 red marbles, 22 green marbles, and 22 yellow marbles. Carol takes 22 marbles from the box at random; then Claudia takes 22 of the remaining marbles at random; and then Cheryl takes the last two marbles. What is the probability that Cheryl gets 22 marbles of the same color?
<spanclass=latexbold>(A)</span>110<spanclass=latexbold>(B)</span>16<spanclass=latexbold>(C)</span>15<spanclass=latexbold>(D)</span>13<spanclass=latexbold>(E)</span>12<span class='latex-bold'>(A) </span>\dfrac1{10}\qquad<span class='latex-bold'>(B) </span>\dfrac16\qquad<span class='latex-bold'>(C) </span>\dfrac15\qquad<span class='latex-bold'>(D) </span>\dfrac13\qquad<span class='latex-bold'>(E) </span>\dfrac12