Question

for a fundraiser, there is a raffle with 200 tickets. One ticket will win a $140 prize, eleven tickets will win a $120 prize, twelve tickets will win a $90 prize, and the remaining tickets will win nothing. If you have a ticket, what is the expected payoff?

Answer 1

Here, we want to get the expected pay off value of having a ticket

To do this, we will have to work with probability

From the question;

one will win $140

11 will win $120

12 will win $90

The rest will win nothing

The number of tickets that will win nothing is;

200-(1+11+12) = 176

The probability of having a ticket that will win $140 is; 1/200

The probability of having a ticket that will win $120 is 11/200

The probability of having a ticket that will win $90 is 12/200

Now, let us calculate the expected value of winning;

We have that as;

$\begin{gathered} (\frac{1}{200}\times140)\text{ + (}\frac{11}{200}\times120)\text{ + (}\frac{12}{200}\times90) \\ \\ =\text{ 0.7 + 6.6 + 5.4 = 12.7} \end{gathered}$

Furthermore, we need the expected value of losing, and with that, we can arrive at the expected payoff