Question

200 lottery tickets are sold for $4 each. The person with the single winning ticket will get $71. What is the expected value for a ticket in this lottery?

Answer 1

From the information given, we have the following;

$\begin{gathered} \text{Cost of ticket}=4 \\ \text{Number of tickets}=200 \\ \text{ Winning prize}=71 \end{gathered}$

Therefore, we can deduce the following;

$\begin{gathered} P\lbrack\text{ winning\rbrack}=\frac{1}{200} \\ P\lbrack lo\sin g\rbrack=\frac{199}{200} \\ \text{ Gain/loss of winning}=67\text{ (that is \ 71-\ 4)} \\ \text{ Gain/loss of losing}=-4 \end{gathered}$

Therefore, the expected value shall be calculated as follows;

$\begin{gathered} Expected\text{ value}=(P\lbrack\text{ winning\rbrack{}x Gain/loss of winning})+(P\lbrack lo\sin g\rbrack\times\text{ Gain/loss of losing} \\ Exp\text{ected value}=(\frac{1}{200}\times\frac{67}{1})+(\frac{199}{200}\times\lbrack-4\rbrack) \\ EV=\frac{67}{200}-\frac{796}{200} \\ EV=-\frac{729}{200} \\ EV=-3.645 \\ \text{Expected value}\approx-3.65\text{ (rounded to the nearest hundredth)} \end{gathered}$

ANSWER:

The expected value of a ticket in this this lottery is -$3.65 (rounded to the nearest hundredth).