Question

You buy a lottery ticket to a lottery that costs $\backslash (10$ per ticket. There are only $100$ tickets available to be sold in this lottery. In this lottery there are one $\backslash )500$ prize, two $\backslash (100$ prizes, and four $\backslash )25$ prizes. Find your expected gain or loss.

Short answer

The expected loss is$-2$.

Step-by-step solution

Given information

A lottery ticket costing $\$10$.

Total tickets sold is $100$.

The prizes are:$1-\$500,2-\$100,4-\$25$.

Explanation

$X$	$P\left(x\right)$	$XP\left(x\right)$
$490$	$\frac{1}{100}$	$490\times \frac{1}{100}=4.9$
$90$	$\frac{2}{100}$	$90\times \frac{2}{100}=4.9$
$15$	$\frac{4}{100}$	$15\times \frac{4}{100}=0.6$
$-10$	$\frac{93}{100}$	$-10\times \frac{93}{100}=-9.3$
Total	$1$	$-2$

$E\left(x\right)=\underset{}{\sum \left[X\times P\left(x\right)\right]}$

X is a random variable that defines the expected profit. There are few options when buying a ticket, the expected profit is $490$because you won $500$and you paid $10$.

So, the difference is $490$. Similarly, there are other probable profits are $90\text{and}15$. If you do not win any prize you will lose $10$.

We will have an expected loss of$-2$.