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8.3 Expected Value

8.3 Expected Value
  • Math Help

    In Example 1, because you pay $1 for a ticket, the payoff if you win $5000 is

    Here are some additional steps for finding the expected value in Example 1.

    Use the Lottery Simulator to answer the Checkpoint question.

  • Consumer Suggestion

    There are currently seven states that do not have a state lottery: Alabama, Alaska, Hawaii, Mississippi, Nevada, Utah, and Wyoming. The most recent state to legalize a state lottery was Arkansas in 2008. To learn more about lotteries in your state, visit

  • Checkpoint Solution

    Sample answers:

    Using the Lottery Simulator, I won 13 times and lost 99,987 times. My total profit was

    Because the expected profit per game is -$0.50, the expected profit for 100,000 games is 100,000(-$0.50) = -$50,000. So, even though I did better than expected, I still lost $35,000. It is clear that playing the Big Four Lottery 100,000 times is not a good way to spend $100,000.

    I do not think there is anything wrong with state lotteries as long as they are honest and not intentionally deceptive. No knowledge of statistics or probability is needed to know that your chances of winning are very small. I do not think state lotteries are a form of regressive tax for the poor because not all poor people play the lottery and not all financially secure people abstain from it.

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