Question

What is $P(E)$ in probability?

Answer 1

Hint: In this question we have to state the definition of $P(E)$ in probability. Also, along with definition, we can state various properties, laws related to $P(E)$ in probability. Here P(E) represents the probability of an event E.

Complete step by step solution:
The term $P(E)$ is the probability of an event $E$. It is also known as the empirical or experimental probability of event $E$.

The formula for finding the probability $P(E)$ is
$P(E) = \dfrac{A}{N}$,
Where, $A$ is the number of trials occurring in the event
$N$ is the total number of trials an individual took for the event.

Probability of any event always lies between $0$ and $1$.

We can write the above condition as $0 < P(E) < 1$. This means that the probability of any event must be greater than $0$ but less than $1$.

If the probability of an event is $0$ i.e., $P(E) = 0$ then we can say that the event does not exist i.e., it is an impossible event.

On the contrary, if the probability of an event is $1$ i.e., $P(E) = 1$, then we can say that the event is certain which means that the event will definitely happen.

Some of the rules related to $P(E)$. Those are:
1. For every event, whose probability we are calculating, $0 < P(E) < 1$ condition satisfies.
2.The addition of probabilities of all the possible events is always $1$
3. If $P(E)$ is given and we need to find its complement i.e., $P(\text{not }E)$ then we can calculate $P(\text{not }E)$ by using formula $P(\text{not }E) = 1 - P(E)$ and vice-versa

Note: We can discuss the possibility of specific problems, or the chances that they will arise, whenever we have concerns about how an event will play out. Statistics is the study of events that follow a probability distribution.
W.K.T, $P(E) = \dfrac{\text{Number of all possible outcomes}}{\text{Number of outcomes favorable to event E}}$​
E is an impossible event, if and only if P(E) = 0.
And E is a sure event, if and only if P(E) = 1.