A standard pair of six-sided dice is rolled. What is the probability of rolling a sum greater than 11
? Express your answer as a fraction or a decimal number rounded to four decimal places.
To find the probability of rolling a sum greater than 11, we need to first identify all the outcomes that would result in a sum greater than 11.
The only combinations that result in a sum greater than 11 are:
- Rolling a 6 on both dice (1/6 probability for each die)
- Rolling a 5 and a 6 (1/6 probability for rolling a 5 and 1/6 probability for rolling a 6)
So, the total number of favorable outcomes is 2.
The total number of possible outcomes when rolling two six-sided dice is 6 * 6 = 36.
Therefore, the probability of rolling a sum greater than 11 is 2/36 = 1/18 ≈ 0.0556.
So, the probability of rolling a sum greater than 11 is approximately 0.0556.