Question

Jeff’s school is selling raffle tickets for $1 each. Of all the money collected from the sale of raffle tickets, 80% will go to a scholarship fund, and 20% will go to the winner of the raffle. Jeff bought 5 of the 750 raffle tickets sold. What is the expected payoff for Jeff when playing the raffle, and what does it mean?
A) –$4, which means that Jeff can expect to lose $4
B) –$1, which means that Jeff can expect to lose $1
C) –$0.80, which means that Jeff can expect to lose $0.80
D) –$4, which does not mean that Jeff can expect to lose $4 – only that he could expect to lose $4 on average if the same scenario were repeated many times

Answer 1

They are selling a total of 750 raffle tickets at 1$ each, therefore they will make 750$. 20% will go to the winner, .20 x 750 = 150
You have to calculate the expected value of Jeffs chances.
Jeff's chances of winning = 5/750 the payoff = 150$
Jeff's chances of losing = 745/750 he would lose 5$ (because he bought 5 tickets)
multiply his chances times the the payoff then add them together
5/750 x 150 + 745/750 x -5
the answer is -4
Since it is asking what this number means the answer is D. If Jeff knows the odds are not in his favor than he expects to lose 5$, there is no way he could only lose 4$, but if Jeff were to repeat the situation many times, on average he would lose 4$