SOLUTION: Ten thousand raffle tickets are sold. One first prize of $ 2 comma 000​, 3 second prizes of $ 600 ​each, and 9 third prizes of $ 400 each are to be​ awarded, with all winne

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Question 1146096: Ten thousand raffle tickets are sold. One first prize of $ 2 comma 000​, 3 second
prizes of $ 600 ​each, and 9 third prizes of $ 400 each are to be​ awarded, with
all winners selected randomly. If you purchase one​ ticket, what are your
expected​ winnings?
Answer by Edwin McCravy(20065)   (Show Source): You can put this solution on YOUR website!
Ten thousand raffle tickets are sold. One first prize of $ 2000​, 3 second prizes
of $600 ​each, and 9 third prizes of $ 400 each are to be​ awarded, with all
winners selected randomly. If you purchase one​ ticket, what are your expected​
winnings?

I will assume this raffle will be conducted like most raffles.  That is, I can't
win more than 1 prize.  The tickets are drawn one at a time without replacing.

The probability of my ticket being drawn to win the $2000 is 1/10000.
My expectation of winning that is ($2000)(1/10000) is $0.20
The probability of my ticket being drawn to win the 1st $600 is 1/9999.
My expectation of winning that is ($600)(1/9999) is $0.0600060006.
The probability of my ticket being drawn to win the 2nd $600 is 1/9998.
My expectation of winning that is ($600)(1/9998) is $0.0600120024.
The probability of my ticket being drawn to win the 3rd $600 is 1/9997.
My expectation of winning that is ($600)(1/9997) is $0.0600180054.
The probability of my ticket being drawn to win the 1st $400 is 1/9996.
My expectation of winning that is ($400)(1/9996) is $0.0400160064.
The probability of my ticket being drawn to win the 2nd $400 is 1/9995.
My expectation of winning that is ($400)(1/9995) is $0.04002001.
The probability of my ticket being drawn to win the 3rd $400 is 1/9994.
My expectation of winning that is ($400)(1/9994) is $0.0400240144.
The probability of my ticket being drawn to win the 4th $400 is 1/9993.
My expectation of winning that is ($400)(1/9993) is $0.0400280196.
The probability of my ticket being drawn to win the 5th $400 is 1/9992.
My expectation of winning that is ($400)(1/9992) is $0.0400320256.
The probability of my ticket being drawn to win the 6th $400 is 1/9991.
My expectation of winning that is ($400)(1/9991) is $0.0400360324.
The probability of my ticket being drawn to win the 7th $400 is 1/9990.
My expectation of winning that is ($400)(1/9990) is $0.04004004.
The probability of my ticket being drawn to win the 8th $400 is 1/9989.
My expectation of winning that is ($400)(1/9989) is $0.0400440485.
The probability of my ticket being drawn to win the 9th $400 is 1/9988.
My expectation of winning that is ($400)(1/9988) is $0.0400480577.

My total expectation is the sum of those, which is:

$ 0.2000000000
$ 0.0600060006
$ 0.0600120024
$ 0.0600180054
$ 0.0400160064
$ 0.0400200100
$ 0.0400240144
$ 0.0400280196
$ 0.0400320256
$ 0.0400360324
$ 0.0400400400
$ 0.0400440485
$ 0.0400480577
--------------
$ 0.7403242630  <--total expectation

Edwin
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