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Two dice are thrown at the same time. Find the probability of getting different numbers on both dice

Solution:

Given, two dice are thrown at the same time.

We have to find the probability of getting a different number on both dice.

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

The possibility of getting different number is

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

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

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

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

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

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

Number of favourable outcomes = 30

Number of possible outcome = 36

Probability = number of favourable outcomes / number of possible outcomes

Probability of getting different number = 30/36

= 10/12

= 5/6

Therefore, the probability of getting a different number is 5/6.

✦ Try This: Three dice are thrown at the same time. Find the probability of getting the same number on all dice.

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

NCERT Exemplar Class 10 Maths Exercise 13.3 Problem 19(ii)

Summary:

Two dice are thrown at the same time. The probability of getting different numbers on both dice is 5/6

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