Problem $8.($Gambler$\text{'}$s Ruin$)$ Consider a coin$-$flipping game with two players where player one wins each toss with prob$-$

ability $p,$ and player two wins with probability $q=1-p.$ Suppose player one has $n_1$ pennies and player two $n_2$ pennies.

Assuming an unfair coin $($ie$,p\frac{1}{2}),$ the probabilities $p_1$ and $p_2$ that players one and two, respectively, will end penniless

are

$p_1=\frac{1-(\frac{p}{q}{)}^{n_2}}{1-(\frac{p}{q}{)}^{n_1+n_2}}$ and $p_2=\frac{1-(\frac{q}{p}{)}^{n_1}}{1-(\frac{q}{p}{)}^{n_1+n_2}}$

Write a program called

gambler.py that accepts $n_1($int$),n_2($int$),$ and $p($float$)$ as command$-$line arguments, and writes the

probabilities $p_1$ and $p_2$ to standard output, separated by a space.

$\_-/$workspace$/$straightline$\_$programs

$ python$3$

gambler.py $101000\mathrm{.}51$

$0\mathrm{.}66618837342006540\mathrm{.}3338116265799349$

$ python$3$

gambler.py $100100\mathrm{.}51$

$0\mathrm{.}0061107125105809030\mathrm{.}9938892874894192$