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Question

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A B C D E A

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

(a) A?

(b) D?

Answer

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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.

.