How much is a VCR/DVD combination player?

Lottery $750 grand prize, 3 digits combination, costs $1 to play what is the expected profit/loss?

• lottery sets up a game wherein a player has a chance of collecting $750. The player must choose a 3-digit number and if it matches, the player receives $750 Remember, 000 is a 3-digit number for lottery draws. It costs $1 to play the game. What is each player's expected profit (or loss)?

• Answer:

  The three digit numbers are: 000, 001,.....999. There are exactly 1000 of them. The player pays $1, If the number is the right one, the player wins $750. There is only 1 way for that to happen. If the number is the wrong one, the player wins $0. There are 999 ways for that to happen. So the expected winnings are (999/1000) * $0 + (1/1000) * $750 = $0.75 The expected profit is: Expected winnings - stake Which is: -25c I.e. an expected loss of 25c. Not as bad as the real lottery.