SOLUTION: A raffle has a grand prize of a European cruise valued at $13000 with a second prize of a Las Vegas getaway valued at $1400. If each ticket costs $2 and 10600 tickets are sold, wh

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Question 1039095: A raffle has a grand prize of a European cruise valued at $13000 with a second prize of a Las Vegas getaway valued at $1400. If each ticket costs $2 and 10600 tickets are sold, what are the expected winnings for a ticket buyer? Express to at least three decimal place accuracy in dollar form (as opposed to cents).
Answer: $

Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
first prize is 13000 and second prize is 1400.
there are 10600 tickets sold.
the probability of getting the grand prize is 1/10600.
the probability of getting the second prize is also 1/10600.

you pay 2 dollars for the ticket.
the probability of winning 13000 is 1/10600.
the probability of winning 1400 is 1/10600.

your expected value is -2 + 1/10600 * 13000 + 1/10600 * 1400.
that equates to expected value of -.641509434.
round that to 3 decimal places and the expected winnings are -.642 dollars.

one way to look at this is as follows:

there are 10600 tickets sold at 2 dollars apiece.
total money shelled out is 10600 * 2 = 21200.
one ticket wins 13000.
one ticket wins 1400.
total value of all tickets sold is therefore -21200 + 13000 + 1400 = -6800
the average gain on each ticket is therefore -6800 / 10600 = -.641509434.
since a negative gains is a positive loss, then the average loss on each ticket is .641509434.
since you were asked for expected winnings, you would report the expected gain which is negative, after you rounded it to 3 decimal places to get -.642.