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

ANSWER

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:

$P(330)=\frac{1}{500}$

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

$P(210)=\frac{9}{500}$

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

$P(30)=\frac{11}{500}$

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

$P(0)=\frac{479}{500}$

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

That means that:

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