SOLUTION: 1000 chances are sold at 6$ a piece for a raffel. there is one grand prize of 400$, two second prizes of 200$, and five third place prizes for 150$. Evaluate the expected value of

Question 1131374: 1000 chances are sold at 6$ a piece for a raffel. there is one grand prize of 400$, two second prizes of 200$, and five third place prizes for 150$. Evaluate the expected value of the lottery.
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

I'm not sure what the meaning is of the phrase "expected value of the lottery". I will assume you mean the expected value of one ticket....

1 first prize; value $400-$6 = $394 (prize minus cost of ticket)
2 second prizes; value each $200-$6 = $194
5 third prizes; value each $150-$6 = $144
992 no prize; value each -$6

The expected value of a ticket is then

The expected value of one ticket is -$4.45.

While that is the classical way to calculate the expected value, based on the definition, there is a much easier path to the answer.

The total cost of the 1000 tickets is $6000, the total payout is $400+$400+$750 = $1550. The expected value of each ticket is

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