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?
- 1/6
- 1/4
- 1/3
- 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.
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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] = \[\frac{\text{ Favourable number of outcomes }}{\text{
Total number of outcomes }} = \frac{6}{36} = \frac{1}{6}\]