Question

What are Equally likely events?

Answer 1

First, we will know about the probability and events. Then we will know about equally likely events. Then We will solve this problem by using some examples.

Complete step by step answer:
The probability is the chance of how likely an event is to occur. The sample space is the set of all possible outcomes. The event is a subset of outcomes of the sample space to which a probability is assigned.
The probability of an event can be Calculated by using the Formula
$P(A) = \dfrac{{Number{\text{ }}of{\text{ }}favourable{\text{ }}events}}{{Total{\text{ }}number{\text{ }}of{\text{ }}the{\text{ }}events{\text{ }}in{\text{ }}the{\text{ }}sample{\text{ }}space}}$ $= \dfrac{{n(E)}}{{n(S)}}$
Equally likely events are the events that have the same probability of occurrence theoretically.
Let us explain by using an example.
Consider we are tossing a dice. A dice has $6$ faces. The possible outcomes while tossing a dice are
$\\{ 1,2,3,4,5,6\\}$
No of sample space,$n(s)$ is $6$
When tossing we get any one of the above outcomes.
Case 1:
Consider we are trying to get ‘$2$’ as an outcome
Then our favorable event is $\\{ 2\\}$
No of a favorable event, $n(E)$ is $1$
We have to find the probability of getting $2$ as an outcome
We calculate the probability of an event by using the formula
$P(A) = \dfrac{{Number{\text{ }}of{\text{ }}favourable{\text{ }}events}}{{Total{\text{ }}number{\text{ }}of{\text{ }}the{\text{ }}events{\text{ }}in{\text{ }}the{\text{ }}sample{\text{ }}space}}$ $= \dfrac{{n(E)}}{{n(S)}}$
$P(A) = \dfrac{1}{6}$
Case 2:
Next, Consider we are trying to get ‘$4$’ as an outcome
Then our favorable event is $\\{ 4\\}$
No of a favorable event, $n(E)$ is $1$
We have to find the probability of getting $4$ as an outcome
We calculate the probability of an event by using the formula
$P(A) = \dfrac{{Number{\text{ }}of{\text{ }}favourable{\text{ }}events}}{{Total{\text{ }}number{\text{ }}of{\text{ }}the{\text{ }}events{\text{ }}in{\text{ }}the{\text{ }}sample{\text{ }}space}}$ $= \dfrac{{n(E)}}{{n(S)}}$
$P(A) = \dfrac{1}{6}$
In both cases, the probability is $\dfrac{1}{6}$
Therefore, these events have the same probability of occurrence. This event is equally likely.

Note:
We should know that the equally likely events have the same probability of occurrence theoretically. If any one of the possible probability is different, it is not an equally likely events
If we are tossing a coin, then We can get either a head or tail.
Here the sample space is $\\{ Head, Tail\\}$
The probability of getting head as an outcome is $\dfrac{1}{2}$ . The probability of getting tail as an outcome is $\dfrac{1}{2}$
Tossing a coin to get heads is also an equally likely event.