Question

In a raffle, one ticket out of 50 will win a $220 prize, one ticket will win a $180 prize, and one ticket will win a $60 prize. The rest will win nothing. If you have a ticket, what is the expected payoff?

Answer 1

Calculate the average of the prizes weighted by the number of tickets to find the expected value of the payoff.

Since there is a total of 50 tickets, from which one wil win a $220 prize, one will win a $180 prize and one will win a $60 prize, then the number of tickets that won't win a prize is 47.

Then, the weighted average of the prizes, is:

$\begin{gathered} \frac{1\times220+1\times180+1\times60+47\times0}{1+1+1+47}=\frac{220+180+60}{50} \\ =\frac{460}{50} \\ =9.2 \end{gathered}$

Therefore, the expected payoff is:

$\text{ \ }9.2$