Two fair dice are rolled together. The probability that the sum rolled is greater that 8 is?
I get 10/36
What is the probability of rolling a sum of 10 on a standard pair of six-sided dice? Express your answer as a fraction or a decimal number rounded to three decimal places, if necessary.
To find the probability that the sum rolled is greater than 8 when two fair dice are rolled together, we need to count the number of favorable outcomes and divide it by the total number of possible outcomes.
Step 1: Determine the favorable outcomes.
To obtain a sum greater than 8, we need the dice to show one of the following combinations:
- A 3 on the first die and a 6 on the second die
- A 4 on the first die and a 5 or 6 on the second die
- A 5 on the first die and a 4, 5, or 6 on the second die
- A 6 on the first die and a 3, 4, 5, or 6 on the second die
So, there are 4 favorable outcomes.
Step 2: Determine the total number of possible outcomes.
Since there are 6 possible outcomes for each die, the total number of possible outcomes when rolling two fair dice is 6 x 6 = 36.
Step 3: Calculate the probability.
To calculate the probability, divide the number of favorable outcomes by the total number of possible outcomes:
Probability = Favorable outcomes / Total outcomes
Probability = 4 / 36 = 1 / 9 ≈ 0.1111
Therefore, the probability that the sum rolled is greater than 8 when two fair dice are rolled together is approximately 0.1111, or 11.11%.