Dice: Finding Expected Values of Games of Chance


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When you roll two six-sided dice, what is the probability of getting a sum of 11?

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1. When two six-sided dice are rolled, what is the probability of getting doubles? (two ones, two twos, etc.)

2. Suppose you play a game with two six-sided dice, where if you get doubles, you win $10, but for anything else you lose $5. If you continue to play this game, how much do you expect to win or lose per roll in the long run? In other words, what is the expected value of this game?

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About This Quiz & Worksheet

Test your ability to calculate probabilities and the expected value of a game of dice in this quiz and worksheet combo. Practice questions focus on probabilities using multiple six-sided, four-sided, and 10-sided dice.

Quiz & Worksheet Goals

In this quiz, you will calculate:

  • Probabilities of getting specific sums with two or more six-sided dice
  • How much you can win or lose in a game of dice
  • Probabilities using dice of different numbers of sides

Skills Practiced

This assessment assesses the following practice skills:

  • Problem solving - use acquired knowledge to solve probability practice problems
  • Defining key concepts - ensure that you can accurately define main phrases, such as chance and probability distribution
  • Knowledge application - use your knowledge to answer questions about calculating expected value

Additional Learning

For more understanding about probabilities, review the lesson Dice: Finding Expected Values of Games of Chance. This lesson examines:

  • Defining and calculating expected value
  • Determining outcomes and probability distributions
  • Results when using more than two dice
  • Using nonstandard dice