Answer:
Explanation:
To find the probability of rolling a pair of dice and not getting a sum of 2 or 12, we need to calculate the probability of all other possible outcomes and then subtract it from 1 (since the sum of all probabilities should be 1).
There are 36 possible outcomes when rolling a pair of dice (6 sides on each die, so 6 * 6 = 36 outcomes). Now, let's count the outcomes that result in a sum of 2 or 12:
Sum of 2: (1, 1) -> Only one outcome
Sum of 12: (6, 6) -> Only one outcome
So, the total outcomes that result in a sum of 2 or 12 are 2.
the probability of getting a sum of 2 or 12 is:
Probability (Sum of 2 or 12) = Number of favorable outcomes / Total possible outcomes
= 2 / 36
= 1 / 18
Now, to find the probability of not getting a sum of 2 or 12, we subtract this probability from 1:
Probability (Not 2 and Not 12) = 1 - Probability (Sum of 2 or 12)
= 1 - (1 / 18)
= (18 - 1) / 18
= 17 / 18
So, the probability of rolling a pair of dice and not getting a sum of 2 or 12 is 17/18.