Question 471066: One thousand raffle tickets are sold for $5.00 each. One grand prize of $800 and two consolation prizes of $100 each will be awarded. Jeremy purchases one ticket. Find his expected value. Show your work for full credit.
(Points : 7)
Answer by ccs2011(207)   (Show Source):
You can put this solution on YOUR website! expected value is a weighted average of all possible outcomes.
Let p be the probability of an outcome.
Let g be the net gain of an outcome.
The expected value of an outcome is the product of p and g.
E = p*g
In this problem there are 3 outcomes: win grand prize, win consolation prize, win nothing.
His total expected value of the raffle ticket is the sum of the expected values from each outcome.
Outcome 1: win grand prize
there are 1000 tickets but only 1 winner, so p = 1/1000
you win $800 but it cost you $5, so g = 795
Outcome 2: win consolation prize
there are 1000 tickets and only 2 winners, so p = 2/1000 or 1/500
you win $100 but it cost you $5, so g = 95
Outcome 3: win nothing
1000-2-1=997, this means 997 tickets do not win, so p = 997/1000
you win 0 but it cost you $5, so g = -5
Now compute Expected Value (EV):
Therefore for every raffle ticket you buy, you should expect to lose $4.
Another way of looking at it is you expect to win $1 for every ticket you buy, but since each one costs $5 its not a very worthwhile investment.
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