MathDB
Do They Meet?

Source:

February 20, 2008
analytic geometryprobabilityinvariant

Problem Statement

Objects AA and BB move simultaneously in the coordinate plane via a sequence of steps, each of length one. Object AA starts at (0,0)(0,0) and each of its steps is either right or up, both equally likely. Object BB starts at (5,7)(5,7) and each of its steps is either left or down, both equally likely. Which of the following is closest to the probability that the objects meet?
<spanclass=latexbold>(A)</span> 0.10<spanclass=latexbold>(B)</span> 0.15<spanclass=latexbold>(C)</span> 0.20<spanclass=latexbold>(D)</span> 0.25<spanclass=latexbold>(E)</span> 0.30 <span class='latex-bold'>(A)</span>\ 0.10 \qquad <span class='latex-bold'>(B)</span>\ 0.15 \qquad <span class='latex-bold'>(C)</span>\ 0.20 \qquad <span class='latex-bold'>(D)</span>\ 0.25 \qquad <span class='latex-bold'>(E)</span>\ 0.30