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Question

Lottery: In the New York State Numbers Lottery, you pay $1 and can bet that the sum of the numbers that come up is 13. The probability of winning is 0.075, and if you win, you win $6.50, which is a profit of $5.50. If you lose, you lose $1. What is the expected value of your profit? Is it an expected gain or an expected loss?

Answer 1

Monica,

the expected value of the game is E=p*w-(1-p)c where w= how much you win and c= how much it cost to play.

Putting the numbers in gives E=.075*6.50-.925*1=.49-.93=-.44. If you play this game 100 times you will be out

(lost) $44. Don't play if you are trying to make money. To make the game "fair" E=0 for a $1 cost to play the winning would have to be p/(1-p)=$12.33.

Jim