What is the sample space of the product of two 6-sided dice where the first number is

Question

2
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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

The sample space is {

Answer 1

When rolling two 6-sided dice, if the first die shows a fixed value of 2, the possible outcomes for the second die will range from 1 to 6.

The resulting products when the first die is 2 can be calculated as follows:

• If the second die is 1: \(2 \times 1 = 2\)
• If the second die is 2: \(2 \times 2 = 4\)
• If the second die is 3: \(2 \times 3 = 6\)
• If the second die is 4: \(2 \times 4 = 8\)
• If the second die is 5: \(2 \times 5 = 10\)
• If the second die is 6: \(2 \times 6 = 12\)

Thus, the products from this setup are: 2, 4, 6, 8, 10, and 12.

So the sample space is:

{ 2 4 6 8 10 12 }