Two dice are tossed. What is the probability that the sum of the numbers on the two dice is a prime number?

$\frac{5}{12}$

We have to find the probability that the sum of the numbers appearing on the dice is a primenumber.

When 2 dice are thrown at the same time, the overall possible outcomes are

(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)

(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)

(3,1) (3,2) (3,3) (3,4) (3,5) (3,6)

(4,1) (4,2) (4,3) (4,4) (4,5) (4,6)

(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)

(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)

Total number of possible outcomes = 36

Favourable outcomes = {(1,1) (1,2) (1,4) (1,6) (2,1) (2,3) (2,5) (3,2) (3,4) (4,1) (4,3) (5,2) (5,6) (6,1) (6,5)}

Number of favourable outcomes = 15

Number of possible outcomes = 36

Probability = number of favourable outcomes / number of possible outcomes

Probability = 15/36 = 5/12