SOLUTION: 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 expect
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Question 365423: 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
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
1,000 tickets sold for 5.00 apiece to bring in 5,000 dollars.
1 grand prize of 800 and 2 consolation prizes of 100 each will be awarded.
jeremy purchases one ticket.
what is his expected value.
he has 1 out of 1000 chances to win 800.
he has 2 out of 1000 chances to win 100.
the expected value is the sum of the net value of each option times the probability that the option will be granted.
in his case:
he spends 5.00 to buy a ticket.
if he wins the pot, then he will receive 800 dollars.
his net value is $800 - $5 = $775 dollars.
if he wins one of the second prizes then he will receive 100 dollars.
his net value is $100 - $5 = $95 dollars.
this can happen 2 times.
if he doesn't win anything, then his net value is -$5.00
the probability that he will win first prize is 1/1000.
the probability that he will win one of the second prizes is 1/1000.
the probability that he will win the other of the second prizes is 1/1000
the probability that he will not win any of the prizes is 997/1000.
The general formula for expected value is:
a1 * p(a1) + a2 * p(a2) + a3 * p(a3) + .....aN * p(aN).
a1 through aN are the net values for each outcome.
p(a1) through p(aN) are the probabilities for each outcome.
for jeremy's problem, the expected value is:
795 * (1/1000) + 95 * (1/1000) + (95/1/1000) + (-5)*(997/1000)
the net result of all of this is that his expected value is -$4.00 dollars.
Looking at this another way, we should be able to come up with the same answers.
he spends $5.00 each time.
1% of the time he will win $800.
2% of the time he will win $100.
97% of the time he will win $0.00.
If he plays the game 1000 times, then:
he will spend $5.00 1000 times for a total of $5,000.00
he will win $800.00 1 time for a total of $800.00
he will win $100.00 2 times for a total of $200.00
he will win nothing 997 times for a total of $0.00
His total net value is $1000 - $5000 = -$4000.
divide that by 1000 and his average net value for each game is -$4.00.
This is the same as the answser we derived from the expected value formula.
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