Question

Two dice are thrown simultaneously. What is the probability that the sum of the numbers appearing on the dice is a prime number.

Answer 1

Finding the probability of the numbers appearing on the dice is a prime number:

Sum of the numbers appearing on the dice is a prime number i.e.,$2,3,5,7$ and $11$.

So, the possible outcomes are $(1,1),(1,2),(2,1),(1,4),(2,3),(3,2),(4,1),(1,6),(2,5),(3,4),(4,3),(5,2),(6,1),(5,6),(6,5).$

Hence, number of possible outcomes$=15$

Therefore the probability that the sum of the numbers appearing on the dice is a prime number $=\frac{15}{36}=\frac{5}{12}$