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} (1*220+1*180+1*60+47*0)/(1+1+1+47)=(220+180+60)/(50) \\ =(460)/(50) \\ =9.2 \end{gathered}`

Therefore, the expected payoff is:

`\text{ \$}9.2`