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Two Dice Probability Charts

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Two Dice Probability Charts

Imagine rolling two fair six-sided dice. Each die shows 1, 2, 3, 4, 5 or 6. Add the two numbers to find the sum. In the chart, the row is the first die and the column is the second die. Use the chart and your probability knowledge to solve the questions.

A chart of all possible sums

Each square shows the sum for one possible pair of dice results. For example, first die 2 and second die 5 gives a sum of 7.

First die ↓ / Second die →

1

2

3

4

5

6

1

2

3

4

5

6

Probability detectives

There are 36 equally likely pairs of results when two fair dice are rolled. Use the chart to investigate which sums are more or less likely.

1.Complete the chart by adding the two dice numbers in every empty square. What number belongs in the square where first die is 4 and second die is 2?
2.Arjun is hoping for a sum of 7. How many different dice-result pairs make 7?
3.Which sum is more likely: 4 or 10? Explain using the number of result pairs.
4.Choose the sum that is most likely when two fair dice are rolled.
  • 2
  • 7
  • 12
  • They are all equally likely
5.Fill in the blank: There is only way to make a sum of 2, but there are ways to make a sum of 7.
6.True or false? A sum of 1 is possible when rolling two six-sided dice. Give a reason.
TrueFalse
7.A game gives one point if the sum is 5. List all the result pairs that score a point.
8.Arlo says, “A sum of 12 is just as likely as a sum of 2.” Is Arlo correct? Explain.
9.A sum is called even if it is divisible by 2. Give two different dice-result pairs that make an even sum.
10.If you rolled the dice 36 times, would you expect to get a sum of 7 exactly 6 times? Explain why this is an expectation, not a guarantee.

3 printable pages

  • Two Dice Probability Charts, page 1 of 3: A chart of all possible sums

    Page 1

  • Two Dice Probability Charts, page 2 of 3: Probability detectives

    Page 2

  • Two Dice Probability Charts, page 3 of 3: 8. Arlo says, “A sum of 12 is just as likely as a sum of 2.” Is Arlo correct? Explain.

    Page 3

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