Question

Two dice are thrown. Find the probability of getting.
(a) The sum of the numbers on their upper faces is at least $9$.
(b) The sum of the numbers on their upper faces is $15$.
(c) The number on the upper face of the second die is greater than the number on the upper face of the first die.

Answer 1

Sum of number is atlesat 9 in cases $(6,3),(5,4),(4,5),(3,6),(6,4),(5,5),(4,6),(5,6),(6,5),(6,6).$

Total number of favorable outcomes$=10$

Total number of outcomes$=36$

Probability $\frac{10}{36}$ $=\frac{5}{18}$

Sum of number on upper face is $15$ is not possible because maximum is $12$

Hence, probability is $0$.

Number number on the upper face of the second die is greater than the number on the upper face of the first die is possible in $(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)$

Total number of favorable outcomes$=15$

Total number of outcomes$=36$

Probability $\frac{15}{36}$ $=\frac{5}{12}$