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Lottery Prize - Probablities

by Tami
(NC)










































A lottery has one $2000 prize, two $1000 prizes, and ten $500 prizes. Two thousand tickets are sold at $5 each. Find the expectation if a person buys two tickets

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Mar 29, 2012
Lottery Prize - Probabilities
by: Staff


Question:

by Tami
(NC)


A lottery has one $2000 prize, two $1000 prizes, and ten $500 prizes. Two thousand tickets are sold at $5 each. Find the expectation if a person buys two tickets


Answer:

P($2000 prize) = 1/2000
P($1000 prize) = 2/2000
P($500 prize) = 10/2000
P(no prize) = (2000 – 1 – 2 – 10)/2000 = 1987/2000

Note: if you purchase a ticket for $5, you have lost $5. If you win a prize the cost of the ticket must be subtracted from the prize money. The $2000 prize becomes $1995, the $1000 prize becomes $995, and the $500 prize becomes $495.



If you buy only 1 ticket, your expected return is:

P(1 ticket profit) = $1995*P($2000 prize) + $995*P($1000 prize) + $495*P($500 prize) + (-$5)*P(no prize)


P(1 ticket profit) = 1995*(1/2000) + 995*(2/2000) + 495*(10/2000) + (-5)*(1987/2000)=-0.50

The expected return of purchasing one lottery ticket for $5 is a loss of 50 cents.

If you buy 2 tickets for $5 each, the expected return to you is a loss of $1.00.

>>> The final answer is: a “loss” of $1.00





Thanks for writing.

Staff
www.solving-math-problems.com


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