Sonia Rowland

## Answered question

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.

### Answer & Explanation

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

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