Question

Out of 125 tickets in a raffle, one ticket will win a $230 prize, one ticket will win a $180 prize, one ticket will win a $110 prize, and one ticket will win a $70 prize. The other tickets will win nothing. If you have a ticket, what is the expected payoff?

Answer 1

Out of 125 tickets in a raffle:

One ticket will win a $230 prize,

Probability of winning $230 prize = 1/125

One ticket will win a $110 prize,

Probability of winning $110 prize = 1/125

One ticket will win a $70 prize,

Probability of winning $70 prize = 1/125

The other tickets will win nothing.

The remaining tickets (125 - 3 = 122) have a payoff of $0

The expected payoff can be calculated by multiplying the payoff with the corresponding probability.

`\begin{gathered} E(x)=\sum x\cdot P(x) \\ E(x)=\$230\cdot(1)/(125)+\$110\cdot(1)/(125)+\$70\cdot(1)/(125)+\$0\cdot(122)/(125) \\ E(x)=\$1.84+\$0.88+\$0.56+\$0 \\ E(x)=\$3.28 \end{gathered}`

Therefore, the expected payoff is $3.28