# Two different dice are tossed together. Find the probability of getting a doublet.

Answer

Verified

328.5k+ views

Hint: A dice has the shape of a cube having one number from 1, 2, 3, 4, 5 and 6 printed on each of the faces of the cube. Getting a doublet means both the numbers on the dice are the same. A dice can have one of the six outcomes from 1, 2, 3, 4, 5 and 6.

Complete step-by-step answer:

We have been given that two dice have been tossed. Since the number of outcomes on a single dice is 6, therefore the total number of outcomes when two dices are tossed will be \[6\times 6=36\]. This is called sample space or the total number of events that may occur. The different outcomes are shown in the table below:

Observing the table carefully, we come to the conclusion that there are six doublets (1,1), (2,2), (3,3), (4,4), (5,5) and (6,6). These are the favourable outcomes. Hence, the number of favourable outcomes is 6.

Therefore we have sample space, denoted by \[n\left( s \right)=36\]. And number of favourable outcomes, denoted by \[n\left( e \right)=6\].

We know that the probability of an event, denoted by \[\text{P}\left( e \right)\] is given by:

$\text{P}(e)=\dfrac{n(e)}{n(s)}........................................(1)$

Here, we have \[n\left( s \right)=36\] and $n(e)=6$.

Substituting these values in equation \[\left( 1 \right)\], we get;

$\text{P}(e)=\dfrac{6}{36}=\dfrac{1}{6}.$

Note: One should properly know the concept of probability and its formula to solve questions. We should understand the meaning of terms like doublet, triplet and likewise. If there would have been three dice, then the total number of outcomes would have been $n(s)=6\times 6\times 6=216$. For $n$ number of dices, the total number of outcomes will be $n(s)={{6}^{n}}$.

Complete step-by-step answer:

We have been given that two dice have been tossed. Since the number of outcomes on a single dice is 6, therefore the total number of outcomes when two dices are tossed will be \[6\times 6=36\]. This is called sample space or the total number of events that may occur. The different outcomes are shown in the table below:

Observing the table carefully, we come to the conclusion that there are six doublets (1,1), (2,2), (3,3), (4,4), (5,5) and (6,6). These are the favourable outcomes. Hence, the number of favourable outcomes is 6.

Therefore we have sample space, denoted by \[n\left( s \right)=36\]. And number of favourable outcomes, denoted by \[n\left( e \right)=6\].

We know that the probability of an event, denoted by \[\text{P}\left( e \right)\] is given by:

$\text{P}(e)=\dfrac{n(e)}{n(s)}........................................(1)$

Here, we have \[n\left( s \right)=36\] and $n(e)=6$.

Substituting these values in equation \[\left( 1 \right)\], we get;

$\text{P}(e)=\dfrac{6}{36}=\dfrac{1}{6}.$

Note: One should properly know the concept of probability and its formula to solve questions. We should understand the meaning of terms like doublet, triplet and likewise. If there would have been three dice, then the total number of outcomes would have been $n(s)=6\times 6\times 6=216$. For $n$ number of dices, the total number of outcomes will be $n(s)={{6}^{n}}$.

Last updated date: 02nd Jun 2023

â€¢

Total views: 328.5k

â€¢

Views today: 4.86k

Recently Updated Pages

Calculate the entropy change involved in the conversion class 11 chemistry JEE_Main

The law formulated by Dr Nernst is A First law of thermodynamics class 11 chemistry JEE_Main

For the reaction at rm0rm0rmC and normal pressure A class 11 chemistry JEE_Main

An engine operating between rm15rm0rm0rmCand rm2rm5rm0rmC class 11 chemistry JEE_Main

For the reaction rm2Clg to rmCrmlrm2rmg the signs of class 11 chemistry JEE_Main

The enthalpy change for the transition of liquid water class 11 chemistry JEE_Main

Trending doubts

Difference Between Plant Cell and Animal Cell

Write an application to the principal requesting five class 10 english CBSE

Ray optics is valid when characteristic dimensions class 12 physics CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Write the 6 fundamental rights of India and explain in detail

Write a letter to the principal requesting him to grant class 10 english CBSE

List out three methods of soil conservation

Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE

Write a letter to the Principal of your school to plead class 10 english CBSE