# Probability of sure event is:

A) 1

B) 0

C) 100

D) 0.1

Answer

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Hint: We need to know about what is meant by event then what does sure event imply then according to that by using the probability formula we can get the result.

\[P\left( A \right)=\dfrac{m}{n}=\dfrac{\text{number of favorable outcomes}}{\text{total number of possible outcomes}}\]

Complete step-by-step answer:

Let us look into some basic definitions at first.

TRIAL: Let a random experiment be repeated under identical conditions then the experiment is called a trial.

OUTCOME: A possible result of a random experiment is called its outcome.

SAMPLE SPACE: The set of all possible outcomes of an experiment is called the sample space of the experiment and is denoted by S.

SAMPLE POINT: The outcome of an experiment is called sample point.

EVENT: A subset of the sample space associated with a random experiment is said to occur, if any one of the elementary events associated to it is an outcome.

SURE EVENT: An event which must occur, whatever be the outcome is called a sure event or certain event.

PROBABILITY: If there are n elementary events associated with a random experiment and m of them are favorable to an event A, then the probability of happening or occurrence of A, denoted by P(A), is given by

\[P\left( A \right)=\dfrac{m}{n}=\dfrac{\text{number of favorable outcomes}}{\text{total number of possible outcomes}}\]

Now, by looking into the definition of sure event we can say that:

Sure event is an event which happens always whenever the experiment is performed.

It implies that the number of favorable outcomes is equal to the total number of possible outcomes.

\[\begin{align}

& \Rightarrow \text{number of favorable outcomes}=\text{total number of possible outcomes} \\

& \Rightarrow m=n \\

& \Rightarrow P\left( A \right)\text{=}\dfrac{m}{n} \\

& \therefore P\left( A \right)\text{=}1\text{ } \\

\end{align}\]

Hence, the correct option is (a).

Note: Consider an example related to sure event, If a dice is rolled then the event of occurring a digit greater than 0 is called sure event .Here, total number of possible outcomes are 6 and the number of favorable outcomes is also 6.

\[\begin{align}

& \Rightarrow m=n=6 \\

& \Rightarrow P\left( A \right)\text{=}\dfrac{m}{n} \\

& \Rightarrow P\left( A \right)\text{=}\dfrac{6}{6} \\

& \therefore P\left( A \right)\text{=}1\text{ } \\

\end{align}\]

It is important to note that in a sure event the number of favorable outcomes is equal to the total number of possible outcomes. Therefore, the probability of a sure event is 1.

We can also directly say that the probability of a sure event is 1 because it should occur whatever may be the outcome but doing it elaborately gives much idea.

\[P\left( A \right)=\dfrac{m}{n}=\dfrac{\text{number of favorable outcomes}}{\text{total number of possible outcomes}}\]

Complete step-by-step answer:

Let us look into some basic definitions at first.

TRIAL: Let a random experiment be repeated under identical conditions then the experiment is called a trial.

OUTCOME: A possible result of a random experiment is called its outcome.

SAMPLE SPACE: The set of all possible outcomes of an experiment is called the sample space of the experiment and is denoted by S.

SAMPLE POINT: The outcome of an experiment is called sample point.

EVENT: A subset of the sample space associated with a random experiment is said to occur, if any one of the elementary events associated to it is an outcome.

SURE EVENT: An event which must occur, whatever be the outcome is called a sure event or certain event.

PROBABILITY: If there are n elementary events associated with a random experiment and m of them are favorable to an event A, then the probability of happening or occurrence of A, denoted by P(A), is given by

\[P\left( A \right)=\dfrac{m}{n}=\dfrac{\text{number of favorable outcomes}}{\text{total number of possible outcomes}}\]

Now, by looking into the definition of sure event we can say that:

Sure event is an event which happens always whenever the experiment is performed.

It implies that the number of favorable outcomes is equal to the total number of possible outcomes.

\[\begin{align}

& \Rightarrow \text{number of favorable outcomes}=\text{total number of possible outcomes} \\

& \Rightarrow m=n \\

& \Rightarrow P\left( A \right)\text{=}\dfrac{m}{n} \\

& \therefore P\left( A \right)\text{=}1\text{ } \\

\end{align}\]

Hence, the correct option is (a).

Note: Consider an example related to sure event, If a dice is rolled then the event of occurring a digit greater than 0 is called sure event .Here, total number of possible outcomes are 6 and the number of favorable outcomes is also 6.

\[\begin{align}

& \Rightarrow m=n=6 \\

& \Rightarrow P\left( A \right)\text{=}\dfrac{m}{n} \\

& \Rightarrow P\left( A \right)\text{=}\dfrac{6}{6} \\

& \therefore P\left( A \right)\text{=}1\text{ } \\

\end{align}\]

It is important to note that in a sure event the number of favorable outcomes is equal to the total number of possible outcomes. Therefore, the probability of a sure event is 1.

We can also directly say that the probability of a sure event is 1 because it should occur whatever may be the outcome but doing it elaborately gives much idea.

Last updated date: 04th Oct 2023

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