Two dice are thrown together the probability of getting the same number on both the dices

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)

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

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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If two identical dice are thrown simultaneously (The order of result does not matter. For example, $(2, 3)$ and $(3, 2)$ are considered same), what is the probability of getting same number on both the dice?

My attempt:
Now the reduced sample space is of size = $6+{6 \choose 2} = 6 + 15 = 21$.

Though the sample space is reduced from $36$ to $21$, the probability of getting the same number on both dice is $\frac{1}{36}$, and the probability of getting different number on both the dice is $\frac{2}{36}$.

Since we have $6$ possibilities of getting same number on both the dice, the required probability is $\frac{6}{36} = \frac{1}{6}$

Two dice are thrown simultaneously. What is the probability of getting the same number on both the dice?

1. 1/6
2. 1/4
3. 1/3
4. 1/9

Answer (Detailed Solution Below)

Option 1 : 1/6

Free

150 Questions 150 Marks 150 Mins

Given:

Two dice are thrown simultaneously

Calculation:

When two dice are thrown simultaneously,

Number of possible outcomes are 36.

If getting the same number on both dice is taken as event,

Then for the 1st event, 

⇒ Number of outcomes are 6.

For 2nd event,

⇒ Number of outcomes/total number of possible outcomes

⇒ 6/(6 × 6)

⇒ 1/6

∴ The probability of getting the same number of both the dice is 1/6.

Last updated on Sep 26, 2022

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Two dice are thrown together. The probability of getting the same number on both dice is

• \[\frac{1}{2}\]

• \[\frac{1}{3}\]

• \[\frac{1}{6}\]

• \[\frac{1}{12}\]

When two dice are thrown together, all 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 outcomes = 36
The favourable outcomes are (1, 1), (2, 2), (3, 3), (4, 4), (5, 5) and (6, 6).
So, the number of favourable outcomes are 6.
∴ P(getting the same number on both dice) = \[\frac{\text{ Favourable number of outcomes }}{\text{ Total number of outcomes }} = \frac{6}{36} = \frac{1}{6}\]

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