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What is the sample space of the sum of two 6-sided dice where the first number is less than

6
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List your values from smallest to largest.

Normally we would put commas when making a list but do not this for the question. Put a single space. Example: instead of

1, 2 we write 1 2

1 answer

To determine the sample space of the sum of two 6-sided dice where the first die shows a number less than 6, we need to consider the possible outcomes for the two dice.

The first die can show the values 1, 2, 3, 4, or 5 (since it must be less than 6). The second die can show any value from 1 to 6.

Now, let's list all possible sums for each value of the first die:

  1. If the first die is 1:

    • 1 + 1 = 2
    • 1 + 2 = 3
    • 1 + 3 = 4
    • 1 + 4 = 5
    • 1 + 5 = 6
    • 1 + 6 = 7

  2. If the first die is 2:

    • 2 + 1 = 3
    • 2 + 2 = 4
    • 2 + 3 = 5
    • 2 + 4 = 6
    • 2 + 5 = 7
    • 2 + 6 = 8

  3. If the first die is 3:

    • 3 + 1 = 4
    • 3 + 2 = 5
    • 3 + 3 = 6
    • 3 + 4 = 7
    • 3 + 5 = 8
    • 3 + 6 = 9

  4. If the first die is 4:

    • 4 + 1 = 5
    • 4 + 2 = 6
    • 4 + 3 = 7
    • 4 + 4 = 8
    • 4 + 5 = 9
    • 4 + 6 = 10

  5. If the first die is 5:

    • 5 + 1 = 6
    • 5 + 2 = 7
    • 5 + 3 = 8
    • 5 + 4 = 9
    • 5 + 5 = 10
    • 5 + 6 = 11

Now let's combine and organize all the sums we obtained:

Summing all individual outcomes, we get the unique possible sums: 2, 3, 4, 5, 6, 7, 8, 9, 10, 11.

Thus, the sample space of the sums of these two dice, where the first number is less than 6, is:

2 3 4 5 6 7 8 9 10 11