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Two dice are thrown at the same time. Determine the probability that the difference of the numbers on the two dice is 2

Solution:

Given, two dice are thrown at the same time.

We have to determine the probability that the difference of the numbers on the two dice is 2.

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

Favourble outcomes to get difference of the numbers on the dice as 2 are

(1,3)

(2,4)

(3,1)(3,5)

(4,2) (4,6)

(5,3)

(6,4)

Number of favourable outcomes = 8

Number of possible outcomes = 36

Probability = number of favourable outcomes / number of possible outcomes

Probability of getting difference of the numbers on the dice as 2 = 8/36

= 4/18

= 2/9

Therefore, the probability of getting the difference of the numbers on the dice as 2 is 2/9.

✦ Try This: Two dice are thrown at the same time. Determine the probability that the difference of the numbers on the two dice is 1.

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

NCERT Exemplar Class 10 Maths Exercise 13.3 Problem 26

Summary:

Two dice are thrown at the same time. The probability that the difference of the numbers on the two dice is 2 is 2/9

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