Question

200 lottery tickets are sold for $2 each. The person with the single winning ticket will get $83. What is the expected value for a ticket in this lottery?

Answer 1

Given:

200 lottery tickets are sold for $2 each

winning ticket will get $83

To determine the expected value, we must the chance of winning the prize first:

The change of winning the price is 1/200.

So, the first expression would be:

$(83-2)(\frac{1}{200})$

Next, we determine the lose as well.

The chance to lose is (199/200). So the second expression is:

$-2(\frac{199}{200})$

Then, we combine the two expressions:

$\begin{gathered} (83-2)(\frac{1}{200})-((2)((\frac{199}{200}) \\ \text{Simplify} \\ =\frac{81}{200}-\frac{199}{100} \\ =-1.585 \end{gathered}$

Therefore, the expected value for a ticket is -$1.585 or the person is expected to lose $1.585.