MathDB
Choosing balls

Source: AMC 10 2006B, Problem 17

February 17, 2006
probabilitysymmetryAMC

Problem Statement

Bob and Alice each have a bag that contains one ball of each of the colors blue, green, orange, red, and violet. Alice randomly selects one ball from her bag and puts it into Bob's bag. Bob then randomly selects one ball from his bag and puts it into Alice's bag. What is the probability that after this process, the contents of the two bags are the same? <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> \frac 1{10} \qquad <span class='latex-bold'>(B) </span> \frac 16 \qquad <span class='latex-bold'>(C) </span> \frac 15 \qquad <span class='latex-bold'>(D) </span> \frac 13 \qquad <span class='latex-bold'>(E) </span> \frac 12