Answer
454.2k+ views
Hint: Use basic definition of probability:
$P\left( E \right)=\dfrac{\text{Total number favourable to cases}}{\text{Total outcomes (sample space)}}$
As we know that $P\left( E \right)=\dfrac{\text{ Number of outcomes required}}{\text{sample space (Total no}\text{. of outcomes)}}$
Here, As we can observe that we have six faces on a die with six letters, i.e., the number of total outcomes will be 6.
Let categorise the number of times letters can come by counting the number of faces at which they are present:
$\begin{align}
& A=2 \\
& B=1 \\
& C=1 \\
& D=1 \\
& E=1 \\
\end{align}$
Hence, for any face’s letter probability
$P\left( E \right)=\dfrac{\text{Outcome of that particular letter}}{\text{Total number of outcomes }}$
(i) Probability for getting $A$
\[\begin{align}
& P\left( E \right)=\dfrac{\text{No}\text{. of times A can come to a face}}{\text{Total number of outcomes possible }} \\
& P\left( E \right)=\dfrac{2}{6}=\dfrac{1}{3} \\
\end{align}\]
(ii) Probability for getting $D$
\[\begin{align}
& P\left( E \right)=\dfrac{\text{No}\text{. of times D can come to a face}}{\text{Total number of outcomes possible }} \\
& P\left( E \right)=\dfrac{1}{6} \\
\end{align}\]
Note: (i) One can take the total number of outcomes as $5$ as counting the number of letters present $A,B,C,D,E$ which will be wrong because we are calculating probability with respect to the faces (once thrown written in the question).
(ii) One can think, this problem belongs to any application part of probability but here it is using the fundamental definition.
$P\left( E \right)=\dfrac{\text{Total number favourable to cases}}{\text{Total outcomes (sample space)}}$
As we know that $P\left( E \right)=\dfrac{\text{ Number of outcomes required}}{\text{sample space (Total no}\text{. of outcomes)}}$
Here, As we can observe that we have six faces on a die with six letters, i.e., the number of total outcomes will be 6.
Let categorise the number of times letters can come by counting the number of faces at which they are present:
$\begin{align}
& A=2 \\
& B=1 \\
& C=1 \\
& D=1 \\
& E=1 \\
\end{align}$
Hence, for any face’s letter probability
$P\left( E \right)=\dfrac{\text{Outcome of that particular letter}}{\text{Total number of outcomes }}$
(i) Probability for getting $A$
\[\begin{align}
& P\left( E \right)=\dfrac{\text{No}\text{. of times A can come to a face}}{\text{Total number of outcomes possible }} \\
& P\left( E \right)=\dfrac{2}{6}=\dfrac{1}{3} \\
\end{align}\]
(ii) Probability for getting $D$
\[\begin{align}
& P\left( E \right)=\dfrac{\text{No}\text{. of times D can come to a face}}{\text{Total number of outcomes possible }} \\
& P\left( E \right)=\dfrac{1}{6} \\
\end{align}\]
Note: (i) One can take the total number of outcomes as $5$ as counting the number of letters present $A,B,C,D,E$ which will be wrong because we are calculating probability with respect to the faces (once thrown written in the question).
(ii) One can think, this problem belongs to any application part of probability but here it is using the fundamental definition.
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Why Are Noble Gases NonReactive class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let X and Y be the sets of all positive divisors of class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x and y be 2 real numbers which satisfy the equations class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x 4log 2sqrt 9k 1 + 7 and y dfrac132log 2sqrt5 class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x22ax+b20 and x22bx+a20 be two equations Then the class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
At which age domestication of animals started A Neolithic class 11 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Which are the Top 10 Largest Countries of the World?
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give 10 examples for herbs , shrubs , climbers , creepers
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference Between Plant Cell and Animal Cell
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Write a letter to the principal requesting him to grant class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Change the following sentences into negative and interrogative class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)