What is the sample space of the sum of two 6-sided die where the first number is less than 4? what is the answer
The sample space of the sum of two 6-sided dice is composed of all the possible outcomes when rolling two dice. Each die has 6 sides, so there are 6 possible outcomes for each die. Hence, there are a total of 36 possible outcomes (6 x 6 = 36) when rolling two dice.
To find the sample space of the sum of two dice where the first number is less than 4, we need to identify all the outcomes where the first number rolled is less than 4. The possible outcomes for the first roll are 1, 2, and 3.
For each of these outcomes, we then need to consider all the possible outcomes for the second roll. Since the second die also has 6 sides, there are 6 possible outcomes for each of the 3 outcomes of the first roll. Therefore, the total number of outcomes when the first number is less than 4 is 3 x 6 = 18.
Hence, the sample space of the sum of two 6-sided dice where the first number is less than 4 has 18 possible outcomes.