Laplace definition on probability:
If an experiment (a trial or operation) can produce a number of different and equally likely outcomes, some of which can be considered favorable, then the probability \(P\) of a favorable happening is defined as the ratio of the number of favorable outcomes to the total number of possible outcomes.
Probability of an event:
Let \(S\) be the sample space and \(E\) be the even, then consider an experiment with \(n\) likely and certain outcomes and outcomes are favorable to event \(E\), then the probability of occurrence of the event E, can be written as \(P(E)\) is given by,
Here the \(n(E)\) means the number of outcomes favoring the occurrence of the even \(E\).
The \(n(S)\) means the total number of possible outcomes of an experiment.
We can also use some other variables for events \(E\) like \(A, B, C\), etc.
Now you know how to find the probability of the particular event. That is,
What if the number of event \(n(E)\) and the probability of event are given \(P(E)\) then how can you find out sample space?
The answer is just rearranging the above formula, and we can find out the sample space or other values as per the requirement. That is,
To find the number of an event if the probability of an event and sample space are given, we can use the formula is,