One thousand raffle tickets are sold for $5.00 each. One grand prize of $1000 and two consolation prizes of $200 each will be awarded. Jeremy purchases one ticket. Find his expected value. Show your work for full credit.
easy way: buy up all the tickets. you spend 1000*$5=$5,000 you win $1000 + $400 for a total of $1400 for a net loss of $5000 - $1400 = $3 600 averaged over the 1000 tickets this is a loss of $3.60 per ticket
so expected value of each ticket is -3.60 i.e. you expect to lose $3.60 for each ticket you buy
you can also use probability if you like, but you will get the same answer and it is somewhat more work
Expected value = sum of probabilities * value Expected value = (1/1000)*(1000)+(2/1000)*(200)+(997/1000)*(0)-5 Expected value = -3.6 So you get the same answer
ok it is not more difficult is it?
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