Question

Every elementary event associated with a random experiment has probability.

Answer 1

Hint:
We can define a sample space and elementary event. Then we can define the probability of an event with its sample space. Then we can find the required solution by combining both the definitions.

Complete step by step solution:
We know that in a statistical experiment, the sample space of the experiment is the set of all the possible outcomes.
We can say that an event is the set of the outcomes in an experiment.
An elementary event is the event which has only one outcome in the sample space of the experiment.
We know that the probability of a random experiment is given by the number of favourable outcomes divided by the total number of outcomes.
In every elementary event of a random experiment, the number of favourable outcomes will be one. We also know that the sample space for all the events in a random experiment is the same.
So, we can say that the probability of all the elementary events of a random experiment are equal.

Therefore, every elementary event associated with a random experiment has equal probability.

Note:
A example for elementary events is given by,
We can take the experiment of tossing a coin as a random experiment.
Its sample space is given by, $S = \left\{ {H,T} \right\}$.
Event of getting a head has only one outcome from the sample space.
So, its probability is given by $\dfrac{1}{2}$ .
Similarly, the event of getting a tail has only one outcome from the sample space.
So, its probability is also given by $\dfrac{1}{2}$ .
As these 2 events have only one outcome each, they are elementary events. But they have equal probabilities.
So, we can say that the probability of all the elementary events of a random experiment are equal.