# 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

### Comments for Lottery Prize - Probablities

 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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