SOLUTION: 8. One thousand raffle tickets are sold for $1.00 each. One grand prize of $200 and two consolation prizes of $50 each will be awarded. Jeremy purchases one ticket. Find his expect

Algebra ->  Probability-and-statistics -> SOLUTION: 8. One thousand raffle tickets are sold for $1.00 each. One grand prize of $200 and two consolation prizes of $50 each will be awarded. Jeremy purchases one ticket. Find his expect      Log On


   

Question 472758: 8. One thousand raffle tickets are sold for $1.00 each. One grand prize of $200 and two consolation prizes of $50 each will be awarded. Jeremy purchases one ticket. Find his expected value. Show your work for full credit.
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
1000 raffle tickets are sold.
997 return nothing.
2 return 50 each.
1 returns 200.
probability of getting nothing back is 997/1000 = .997
probability of getting 50 back is 2/1000 = .002
probability of getting 200 back is 1/1000 = .001
he expects to get back:
.997 * 0 + .002 * 50 + .001 * 200 = .3 = 30 cents.
since he paid 1.00 for the ticket, then his total expected value is -.7.
this means that he will lose 70 cents per ticket on the average.
assume he bought all 1000 tickets.
he would be out 1000 dollars.
he would get nothing back on 997 of them.
he would get 50 back on 2 of them for 100 dollars.
he would get 200 back on 1 of them for 100 dollars.
his net value for the 1000 tickets would be - 700.
divide that by 1000 to get an average of -.7 per ticket.
you could have also looked at it as follows:
.997 of the time he would be - 1.00 (buys ticket and gets nothing back).
.002 of the time he would be + 49 (gets back 50 but loses 1).
.001 of the time he would be + 199 (gets back 200 but loses 1).
total expected value would be:
.997 * (-1) + .002 * (49) + .001 * (199) = -.7