Question

There is a raffle with 100 tickets. One ticket will win a $700 prize, one ticket will win a $510 prize, one ticket will win a $490 prize, and the remaining tickets will win nothing. If you have a ticket, what is the expected payoff?

Answer 1

ANSWER

$\text{\ 17}$

EXPLANATION

We want to find the expected payoff.

To do this, we have to first find the probability of winning each prize:

=> 1 ticket out of 100 will win $700 prize. The probability of winning this prize is:

$P(700)=\frac{1}{100}$

=> 1 ticket out of 100 will win $510 prize. The probability of winning this prize is:

$P(510)=\frac{1}{100}$

=> 1 ticket out of 100 will win $490 prize. The probability of winning this prize is:

$P(490)=\frac{1}{100}$

=> The remaining tickets (97) will win nothing ($0). The probability of winning $0 is:

$P(0)=\frac{97}{100}$

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

$\begin{gathered} E(X)=\Sigma\mleft\lbrace X\cdot P(X\mright)\} \\ \Rightarrow E(X)=(\frac{1}{100}\cdot700)+(\frac{1}{100}\cdot510)+(\frac{1}{100}\cdot490)+(\frac{97}{100}\cdot0) \\ E(X)=7+5.10+4.90+0 \\ E(X)=\text{ \ 17} \end{gathered}$

That is the expected payoff.