MathDB
Leapfrog

Source: 2019 AMC 12B #16

February 14, 2019
2019 AMC2019 AMC 12B

Problem Statement

There are lily pads in a row numbered 0 to 11, in that order. There are predators on lily pads 3 and 6, and a morsel of food on lily pad 10. Fiona the frog starts on pad 0, and from any given lily pad, has a 12\tfrac{1}{2} chance to hop to the next pad, and an equal chance to jump 2 pads. What is the probability that Fiona reaches pad 10 without landing on either pad 3 or pad 6?
<spanclass=latexbold>(A)</span>15256<spanclass=latexbold>(B)</span>116<spanclass=latexbold>(C)</span>15128<spanclass=latexbold>(D)</span>18<spanclass=latexbold>(E)</span>14<span class='latex-bold'>(A) </span> \frac{15}{256} \qquad <span class='latex-bold'>(B) </span> \frac{1}{16} \qquad <span class='latex-bold'>(C) </span> \frac{15}{128}\qquad <span class='latex-bold'>(D) </span> \frac{1}{8} \qquad <span class='latex-bold'>(E) </span> \frac14