[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]

We have seen that, in playing roulette at Monte Carlo

(Example \ref {exam 6.7}), betting 1 dollar on red or 1 dollar on 17 amounts to choosing between the distributions

[[math]] m_X = \pmatrix{ -1 & -1/2 & 1 \cr 18/37 & 1/37 & 18/37\cr } [[/math]]

or

[[math]] m_X = \pmatrix{ -1 & 35 \cr 36/37 & 1/37 \cr } [[/math]]

You plan to choose one of these methods and use it to make 100 1-dollar bets using the method chosen. Using the Central Limit Theorem, estimate the probability of winning any money for each of the two games. Compare your estimates with the actual probabilities, which can be shown, from exact calculations, to equal .437 and .509 to three decimal places.