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# Probability of sure event is:A) 1B) 0C) 100D) 0.1

Last updated date: 15th Mar 2023
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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.
$P\left( A \right)=\dfrac{m}{n}=\dfrac{\text{number of favorable outcomes}}{\text{total number of possible outcomes}}$

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.