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

Question

4
4?

Answer 1

The possible outcomes when the first number is less than 4 are when the first die shows a 1, 2, or 3. In each of those cases, the second die can show any number from 1 to 6.

Therefore, the sample space for the sum of two 6-sided dice where the first number is less than 4 is: {2, 3, 4, 5, 6, 7, 3, 4, 5, 6, 7, 8, 4, 5, 6, 7, 8, 9}

Which simplifies to: {2, 3, 4, 5, 6, 7, 8, 9}