SOLUTION: One hundred tickets are sold for a movie at the cost of $10 each. Some tickets have cash prizes as a part of a promotional campaign. There is one prize of $50, three prizes of $25,

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Question 993908: One hundred tickets are sold for a movie at the cost of $10 each. Some tickets have cash prizes as a part of a promotional campaign. There is one prize of $50, three prizes of $25, and five prizes of $20. What is the expected gain if you buy one ticket? 
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
one hundred tickets are sold at 10 dollars apiece.

1 prize at 50
3 prices at 25
5 prizes at 20.

probability of winning 50 is 1/100.
probability of winning 25 is 3/100.
probability of winning 20 is 5/100.

your expected gain is -10 + (1/100 * 50) + (3/100 * 25) + (5/100 * 20).

that is equal to -7.75 dollars.

your are expected to lose 7.75 dollars for every 10 dollar ticket you buy.

does this make sense?

let's see.

suppose you bought all 100 tickets.

your cost would be 10 * 100 = 1000 dollars.
you would win 1 * 50 + 3 * 25 + 5 * 20 = 50 + 75 + 100 = 225 dollars.

you lost 1000 dollars and you gained 225 dollars, so your net gain is -775 dollars.

a negative net gain is a positive net loss.

you lost 775 dollars.


take the 775 dollars and divide it by 100 and you lost an average of 7.75 on each ticket.

your net loss is an average of 7.75 on each ticket.

your net gain is an average of -7.75 on each ticket.

i believe they were asking for expected gain on one ticket.

that answer is -7.75.