Question:
Find the probability of getting the sum of two numbers, less than 3 or more than 11, when a pair of distinct dice is thrown together.
Solution:
Favorable outcomes for sum of numbers on dice less than 3 or more than 11 are (1,1), (6,6).
Required probability $=\mathrm{P}($ sum is less than 3 or more than 11$)=\frac{2}{36}=\frac{1}{18}$.