SOLUTION: a lottery offers one $1000 prize, two $700 prizes, three $300 prizes, and four $200 prizes. One thousand tickets are sold at $6.00 each. Find the expectation if a pers

Question 1119617: a lottery offers one $1000 prize, two $700 prizes, three $300 prizes, and four $200 prizes.

One thousand tickets are sold at $6.00 each.

Find the expectation if a person buys four tickets.

Assume that the player's ticket is replaced after each draw and that the same ticket can win more than one prize. Round to two decimal places. question 12
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
one prize worth 1000 dollars.
two prizes worth 700 dollars each.
three prizes worth 300 dollars each.
four prizes worth 200 dollars each.

one thousand tickets sold at 6 dollars each.

probability of winning 1000 dollars on a ticket is equal to 1/1000.
probability of winning 700 dollars on a ticket is equal to 2/1000.
probability of winning 300 dollars on a ticket is equal to 3/1000.
probability of winning 200 dollars on a ticket is equal to 4/1000.

the expectation for that one ticket is therefore:

1/1000 * 1000 + 2/1000 * 700 + 3/1000 * 300 + 4/1000 * 200 - 6.

that is equal to -1.9 dollars.

since the tickets can be reused, then each time the probability remains the same.

his total probability is therefore 4 * -1.9 = -7.6 dollars.

suppose that, for some reason, he bought all 1000 tickets.

he's guaranteed to win all the prizes but he has to pay for all the tickets.

he will gain 1000 + 2 * 700 + 3 * 300 + 4 * 100 = 4100, but he will lose
1000 * 6 = 6000 dollars.

his expectation is therefore 4100 - 6000 = -1900.

divide that by the 1000 tickets and the loss averages out to 1.9 dollars on each ticket.

that would be his expectation on each ticket that he buys.

he buys 4.

4 * an average lose of 1.9 on each ticket means a total average loss of 7.6 dollars.

if the tickets are not replaced on each draw, then the probabilities on each draw change.

since they are replaced, the probabilities remain the same on each draw.

i believe that's your answer.

hopefully it's correct.

if not, then let me know what the correct answer should be, since i haven't seen a problem like this one before.

usually it's the expectation on one draw.

replacing the ticket does keep the expectation on each draw the same, which is why i'm assuming the expectation is 4 * the expectatikon on 1 draw.

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