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anonymous
 one year ago
1. A group holds a raffle to raise money. They sell 100 raffle tickets for $5 each. There is one grand prize worth $100, three second place prizes worth $25 each and five 3rd place prizes worth $10 each. Find the expected value associated with the purchase of one ticket. (Remember to subtract the cost of playing from your winnings)
anonymous
 one year ago
1. A group holds a raffle to raise money. They sell 100 raffle tickets for $5 each. There is one grand prize worth $100, three second place prizes worth $25 each and five 3rd place prizes worth $10 each. Find the expected value associated with the purchase of one ticket. (Remember to subtract the cost of playing from your winnings)

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Valpey
 one year ago
Best ResponseYou've already chosen the best response.0Okay, how much do they collect in ticket sales, and how much in total do they pay out in prizes?

Valpey
 one year ago
Best ResponseYou've already chosen the best response.0Yes, they collect $500 in ticket sales but they must pay out prizes of $100 plus 3*$25 = $75 plus 5*$10=$50 or $225 in total prizes.

Valpey
 one year ago
Best ResponseYou've already chosen the best response.0So the gross expected value of a ticket is the total prize pool divided by the number of tickets. The net expected value (what the question is asking) is that amount minus the cost of buying a ticket.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so the answer is 2.25?

Valpey
 one year ago
Best ResponseYou've already chosen the best response.0The people buying the tickets aren't expecting to profit (unless they have unrealistic expectations about luck or something). They are choosing a fun way of donating money to the Group. They are expecting to lose money, or we can say the expected value of a ticket is negative. The raffle is a fund raiser and the person purchasing the ticket can think of $2.75 going toward the Group and the $2.25 going toward the prize pool.

Valpey
 one year ago
Best ResponseYou've already chosen the best response.0But in terms of the answer to the question, it is the amount that a person buying a ticket expects to lose, so $2.25  $5.00.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Oh... I still confused about it... Do I need to use the probability to calculate it? Such as I have \[\frac{ 1 }{ 100 }\] chance to get $100?

Valpey
 one year ago
Best ResponseYou've already chosen the best response.0You could do it that way for each prize, but it will end up the same.

Valpey
 one year ago
Best ResponseYou've already chosen the best response.0You will see that \(\frac{1}{100}*$100+\frac{3}{100}*$25+\frac{5}{100}*$10=$2.25\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I gotcha! Thank you so much!
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