Question

in a raffle, one ticket out of 500 will win a $330 prize, nine tickets will win a $210 prize, and eleven tickets will win a $30 prize. The remaining tickets will win nothing. If you have a ticket, what is the expected payoff?

Answer 1

Step-by-step explanation

The first step is to find the probability of receiving each prize.

We have that:

=> One ticket out of 500 will win a $330 prize. This means that the probability of winning a $330 prize is:

`P(330)=(1)/(500)`

=> Nine tickets out of 500 wil win a $210 prize. This means that the probability of winning a $210 prize is:

`P(210)=(9)/(500)`

=> Eleven tickets out of 500 will win a $30 prize. This means that the probability of winning a $30 prize is:

`P(30)=(11)/(500)`

=> The remaining (479 out of 500) will win nothing ($0). This means that the probability of winning $0 is:

`P(0)=(479)/(500)`

The expected value is the sum of the product of each possible outcome and its corresponding probability.

That means that: