Question 1170625: A charity raffle told people that they should expect to win at least $4 for every ticket they purchase. There were two $50 gift certificates, seven $20 gift certificates, and eleven $15 gift certificates. If there were 150 tickets sold and each ticket sold for $10, were they honest with their customers? If not, how could you make their claim true? Explain/justify your answer.
(can you provide the equation I should use to solve this and explain why because I am struggling to understand what probability equation should be used. Thank you.)
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! Amount raised $1500 (150*$10)
150 tickets, so at $4/ticket expected value, this should mean $600 in prizes.
2-$50=$100
7-$20=$140
11-$15=$165
That is $405, and about $3.70 per ticket
expected value is $50(2/150)+$20(7/150)+$15(11/150)=
$100/150 or $0.67
$140/150 or $0.93
$165/150 or $1.10
that is $2.70
minus $10.00 paid and that means the expected value of a $10 ticket is -$7.30
This is not honest. They could try the truth: here is how much the prizes are worth, and here is how many tickets are being sold. If you bought every ticket, you would lose $1095, which is what is going to the charity. It's a charity raffle.
The other issue is that winning $4 for each ticket makes people think they are getting back the original price of the ticket, which they are not. To win $4 per ticket, which isn't really right, means you first have to pay $10 for that privilege.
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