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Sagot :
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.
[tex]\begin{gathered} E(x)=\sum x\cdot P(x) \\ E(x)=\$230\cdot\frac{1}{125}+\$110\cdot\frac{1}{125}+\$70\cdot\frac{1}{125}+\$0\cdot\frac{122}{125} \\ E(x)=\$1.84+\$0.88+\$0.56+\$0 \\ E(x)=\$3.28 \end{gathered}[/tex]Therefore, the expected payoff is $3.28
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