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

**Solution:**

Given, two dice are thrown simultaneously.

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

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

Therefore, the probability of getting a sum of a prime number is 5/12.

**✦ Try This: **Two dice are thrown simultaneously. What is the probability that the sum of the numbers appearing on the dice is a even number?

**☛ Also Check: **NCERT Solutions for Class 10 Maths Chapter 14

**NCERT Exemplar Class 10 Maths Exercise 13.3 Problem 20(ii)**

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

**Summary:**

Two dice are thrown simultaneously. The probability that the sum of the numbers appearing on the dice is a prime number is 5/12

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