# A child has a die whose six faces show the letters as given below

A B C D E A

The die is thrown once. What is the probability of getting

(a) A?

(b) D?

Answer

Verified

379.5k+ views

Hint:If the die was thrown once, it has six possible outcomes- A, B, C, D, E. To find the probability of an event, we need to divide the number of favorable outcomes by the total number of all possible outcomes. Thus, probability of an event E is given by

$P(E)=\dfrac{n(E)}{n(S)}$

where,

n(E) is the number of favorable outcomes for event E to occur

n(S) is the total number of all possible outcomes (also called sample space)

For this experiment $n(S)=5$

Complete step by step answer:

(a) Here the event E is getting A which is possible in two ways since A is on two faces. Therefore,

$\begin{align}

& n(E)=2 \\

& P(E)=\dfrac{2}{5} \\

\end{align}$

(b) Here the event E is getting D which is possible only when dice shows D. Therefore,

$\begin{align}

& n(E)=1 \\

& P(E)=\dfrac{1}{5} \\

\end{align}$

Thus, answer for (a) is $\dfrac{2}{5}$ and for (b) is also $\dfrac{1}{5}$

Note: A sample space and an event has much better explanation when represented in the form of a set. Then, sample S is a set having all the possible outcomes of an experiment as its elements while event E is the set of all possible outcomes. Event E is a subset of sample space S. It is very important to define the terms experiment, event and sample space very precisely in probability theory.

.

$P(E)=\dfrac{n(E)}{n(S)}$

where,

n(E) is the number of favorable outcomes for event E to occur

n(S) is the total number of all possible outcomes (also called sample space)

For this experiment $n(S)=5$

Complete step by step answer:

(a) Here the event E is getting A which is possible in two ways since A is on two faces. Therefore,

$\begin{align}

& n(E)=2 \\

& P(E)=\dfrac{2}{5} \\

\end{align}$

(b) Here the event E is getting D which is possible only when dice shows D. Therefore,

$\begin{align}

& n(E)=1 \\

& P(E)=\dfrac{1}{5} \\

\end{align}$

Thus, answer for (a) is $\dfrac{2}{5}$ and for (b) is also $\dfrac{1}{5}$

Note: A sample space and an event has much better explanation when represented in the form of a set. Then, sample S is a set having all the possible outcomes of an experiment as its elements while event E is the set of all possible outcomes. Event E is a subset of sample space S. It is very important to define the terms experiment, event and sample space very precisely in probability theory.

.

Recently Updated Pages

Basicity of sulphurous acid and sulphuric acid are

Why should electric field lines never cross each other class 12 physics CBSE

An electrostatic field line is a continuous curve That class 12 physics CBSE

What are the measures one has to take to prevent contracting class 12 biology CBSE

Suggest some methods to assist infertile couples to class 12 biology CBSE

Amniocentesis for sex determination is banned in our class 12 biology CBSE

Trending doubts

The lightest gas is A nitrogen B helium C oxygen D class 11 chemistry CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

Which place is known as the tea garden of India class 8 social science CBSE

What is pollution? How many types of pollution? Define it

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

Give 10 examples for herbs , shrubs , climbers , creepers

Draw a diagram of a plant cell and label at least eight class 11 biology CBSE