[math] \newcommand{\NA}{{\rm NA}} \newcommand{\mat}[1]{{\bf#1}} \newcommand{\exref}[1]{\ref{##1}} \newcommand{\secstoprocess}{\all} \newcommand{\NA}{{\rm NA}} \newcommand{\mathds}{\mathbb}[/math]

Assume that you are playing craps with dice that are loaded in the

following way: faces two, three, four, and five all come up with the same probability [math](1/6) + r[/math]. Faces one and six come up with probability [math](1/6) - 2r[/math], with [math]0 \lt r \lt .02[/math]. Write a computer program to find the probability of winning at craps with these dice, and using your program find which values of [math]r[/math] make craps a favorable game for the player with these dice.