Question 462510: A raffle has $5 tickets and is selling 2000 of these tickets. The prizes are 1st place: $1000 in cash, 2nd place: 5 - $300 cash , and 3rd place 10 - $100 cash. Tickets will be drawn randomly once all the tickets are sold. If you buy 1 ticket, what is your expected value? Enter just the number as a dollar amount, rounded to the nearest cent (if necessary). No $ sign please.
Answer by Edwin McCravy(20060)   (Show Source):
You can put this solution on YOUR website! A raffle has $5 tickets and is selling 2000 of these tickets. The prizes are 1st place: $1000 in cash, 2nd place: 5 - $300 cash , and 3rd place 10 - $100 cash. Tickets will be drawn randomly once all the tickets are sold. If you buy 1 ticket, what is your expected value? Enter just the number as a dollar amount, rounded to the nearest cent (if necessary). No $ sign please.
There are 16 winning tickets and therefore
2000-16 or 1984 losing tickets. You must subtract
the price of the ticket from the winnings:
Prizes Probability
x P(x) x*P(x)
995 1/2000 995/2000
295 5/2000 1475/2000
95 10/2000 950/2000
-5 1984/2000 -9920/2000
-------------------------------------
Totals 1 -6500/2000 = -$3.25
If this identical raffle were held many times and you entered
every time, you would expect to average losing $3.25 per time
you entered in the long run.
Edwin
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