Question 652259: Five thousand raffle tickets are to be sold at $10 each to benefit a local community group. The prizes, the number of each prize to be given away, and the dollar value of winnings for each prize are as follows:
Prize Number to Be
Given Away Dollar Value
Automobile 1 $20,000
Entertainment center 2 3,000 each
DVD recorder 5 400 each
Gift certificate 50 20 each
If you buy one ticket, calculate your expected winnings. (Form the probability distribution of x = your dollar winnings, and remember to subtract the cost of your ticket.
i have tried many different ways. i've tried
Auto 0.0002 20000 10 19990
ente center 0.0004 3000 10 2990
dvd 0.001 400 10 390
gift cerft 0.01 20 10 10
19990(.0002)+ 2990(.0004)+ 390(.001)+ 10(.01) 5.684
3.998 1.196 0.39 0.1 5.684
396010000(.0002)+ 8940100(.0004)+ 152100(.001)+ 100(.01) 82931.14
79202 3576.04 152.1 1 82931.14
82931.14- (5.684)^2 82898.83
SQUARE ROOT 82898.83
287.922
Answer by wkopetzky(1)   (Show Source):
You can put this solution on YOUR website! The part you are missing is all of the non-winning tickets. It should look like this.
X (px)
auto 19990 1/5000 .0002
entertainment
center 2990 2/5000 .0004
DVD recorder 390 5/5000 .001
Gift Cert 10 50/5000 .01
Non-winning
ticket -10 4943/5000 .9886
Remember the ticket cost $10 so on a non-winning ticket you are minus 10. There are 57 prizes so 4943 tickets sold will not win anything (5000-57 = 4943).
Finding the mean of X will give you the average winning of one ticket.
19990(.0002) + 2990(.0004) + 390(.001) + 10(.01) + (-10)(.9886)
3.998+1.196+.39+.1+(-9.886)= -4.202
So the average expected winning on one ticket is -$4.20
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