[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]

Write a program to compute the probability [math]w_x[/math] of Exercise for given values of [math]x[/math], [math]p[/math], and [math]T[/math]. Study the probability that the gambler will ruin the bank in a game that is only slightly unfavorable, say [math]p = .49[/math], if the bank has significantly more money than the gambler.