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 }