What is the sample space of the sum of two 6-sided die where the first number is less than 4 4?
The sample space of the sum of two 6-sided die is the set of all possible outcomes when rolling two dice. Each die has 6 possible outcomes, so the total number of outcomes is 6 * 6 = 36.
For the first number to be less than 4, it can be 1, 2, or 3. This means that the second number can be any number from 1 to 6.
So the sample space of the sum of two 6-sided dice where the first number is less than 4 is the set of all possible sums of rolling a number less than 4 on the first die and any number on the second die.
The possible sums are: 1 + 1, 1 + 2, 1 + 3, 1 + 4, 1 + 5, 1 + 6,
2 + 1, 2 + 2, 2 + 3, 2 + 4, 2 + 5, 2 + 6,
3 + 1, 3 + 2, 3 + 3, 3 + 4, 3 + 5, 3 + 6.
This gives us a total of 18 possible outcomes in the sample space.