Sonia Rowland

2022-09-01

In the Georgia Cash 3 lottery game, your probability of winning is 0.001. The game is played twice daily, so 180 games are played in three months. If you play twice a day for three months, what is the probability that you win exactly twice? Round your answer to four decimal places.

Shane Middleton

Beginner2022-09-02Added 7 answers

This is a binomial distribution question with

$n=180$

$p=0.001$

$q=1-p=0.999$

where

$P(X=x)=\left(\begin{array}{c}x\\ n\end{array}\right){p}^{x}{q}^{n-x}\phantom{\rule{0ex}{0ex}}P(X=2),n=180,p=0.001\phantom{\rule{0ex}{0ex}}X\sim Binomial(n=180,p={0.001}^{2}X=2)\phantom{\rule{0ex}{0ex}}P(X=2)=\left(\begin{array}{c}180\\ 2\end{array}\right){0.001}^{2}{0.999}^{180-2}\phantom{\rule{0ex}{0ex}}P(X=2)={\mathrm{16110.00.001}}^{2}{0.999}^{178}=\mathrm{16110.00.00.8369}\phantom{\rule{0ex}{0ex}}P(X=2)=0.0135$

$n=180$

$p=0.001$

$q=1-p=0.999$

where

$P(X=x)=\left(\begin{array}{c}x\\ n\end{array}\right){p}^{x}{q}^{n-x}\phantom{\rule{0ex}{0ex}}P(X=2),n=180,p=0.001\phantom{\rule{0ex}{0ex}}X\sim Binomial(n=180,p={0.001}^{2}X=2)\phantom{\rule{0ex}{0ex}}P(X=2)=\left(\begin{array}{c}180\\ 2\end{array}\right){0.001}^{2}{0.999}^{180-2}\phantom{\rule{0ex}{0ex}}P(X=2)={\mathrm{16110.00.001}}^{2}{0.999}^{178}=\mathrm{16110.00.00.8369}\phantom{\rule{0ex}{0ex}}P(X=2)=0.0135$

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