Question

Determine the probability of rolling a multiple of 2 or a multiple of 3 with a single 12-sided die. Leave your answer in a reduced fraction. Show evidence of your work by typing out your full solution.

Answer 1

To find the probability of rolling a multiple of 2 or 3 with a 12-sided die, we count the favorable outcomes and divide by the total number of possible outcomes. The probability is 3/4.

Step-by-step explanation:

To determine the probability of rolling a multiple of 2 or a multiple of 3 with a single 12-sided die, we need to find the number of favorable outcomes and divide it by the total number of possible outcomes.

First, we list down the multiples of 2 and multiples of 3 on a 12-sided die:

• Multiples of 2: 2, 4, 6, 8, 10, 12 (total of 6 outcomes)
• Multiples of 3: 3, 6, 9, 12 (total of 4 outcomes)

Next, we calculate the total number of favorable outcomes, which is the sum of the favorable outcomes for multiples of 2 and multiples of 3 minus the common outcome of 6:

Total favorable outcomes = 6 + 4 - 1 = 9

Finally, we divide the favorable outcomes by the total number of possible outcomes:

Probability = Favorable outcomes / Total possible outcomes = 9 / 12 = 3 / 4

Therefore, the probability of rolling a multiple of 2 or a multiple of 3 with a single 12-sided die is 3/4.