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Carnival Game Probability Challenge

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Carnival Game Probability Challenge

Work out the chance of winning each game. Give probabilities as fractions, decimals and percentages, then compare the games. Assume every listed outcome is equally likely. Round recurring decimals and percentages to one decimal place.

A worked example

A fair six-sided die has six possible results. If you win by rolling a 1 or a 4, there are two winning results. So the probability is 2/6 = 1/3 = 0.333… ≈ 33.3%. Use: probability = number of winning outcomes ÷ total possible outcomes.

Game A: Lucky Spinner

The spinner has 8 equal sections labelled 1 to 8. You win if it stops on 2, 5 or 7.

1.For Lucky Spinner, write the probability of winning as a fraction in simplest form.
2.For Lucky Spinner, convert the probability of winning to a decimal. Show the division you use.
3.For Lucky Spinner, write the probability of winning as a percentage.
4.Is winning on Lucky Spinner more likely than not? Choose one.
  • Yes, because the probability is greater than 1/2.
  • No, because the probability is less than 1/2.

Game B: Prize Cards

A standard deck contains 52 cards: 4 suits, with 13 cards in each suit. You draw one card at random and win if it is an ace or a jack.

5.For Prize Cards, find the probability of winning as a fraction in simplest form.
6.For Prize Cards, convert the probability of winning to a decimal. Show your calculation.
7.For Prize Cards, convert the probability of winning to a percentage, rounded to one decimal place.
8.Compare Prize Cards with Lucky Spinner. Is the chance of winning Prize Cards greater than the chance of winning Lucky Spinner?
  • Yes
  • No

Game C: Two-Dice Toss

Roll two fair six-sided dice. You win if their total is 6 or 10. There are 36 equally likely ordered pairs of results. Use the two square drawing spaces to sketch the dice.

9.For Two-Dice Toss, list the ordered pairs that give a total of 6 or 10, then write the probability of winning as a fraction in simplest form.
10.For Two-Dice Toss, convert the chance of winning to a decimal. Show your calculation.
11.For Two-Dice Toss, convert the chance of winning to a percentage, rounded to one decimal place.

Game

Fraction

Decimal

Percentage

Lucky Spinner

Prize Cards

Two-Dice Toss

12.Rank Lucky Spinner, Prize Cards and Two-Dice Toss from the greatest probability of winning to the smallest.
13.Which game would you choose if your only aim were to have the greatest chance of winning? Support your choice with the probability values.
14.Invent a fair game with the same chance of winning as Prize Cards. Describe the equally likely outcomes and identify which outcomes win. Show how they give the same probability.

3 printable pages

  • Carnival Game Probability Challenge, page 1 of 3: A worked example, Game A: Lucky Spinner

    Page 1

  • Carnival Game Probability Challenge, page 2 of 3: Game B: Prize Cards, Game C: Two-Dice Toss

    Page 2

  • Carnival Game Probability Challenge, page 3 of 3: 11. For Two-Dice Toss, convert the chance of winning to a percentage, rounded to one…

    Page 3

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