Here you will learn what is the probability of an event formula with examples.
Let’s begin –
Probability of an Event
Definition : If there are n elementary events associated with a random experiment and m of them are favourable to an event A, then the probability of happening or occurrence of A is denoted by P(A) and is defined as ratio \(m\over n\).
Thus, Probability of an Event = P(A) = \(number of favourable event\over total number of elementary events\)
\(P(A)\) = \(m\over n\)
Clearly, 0 \(\le\) m \(\le\) n. Therefore,
0 \(\le\) \(m\over n\) \(\le\) 1
\(\implies\) 0 \(\le\) P(A) \(\le\) 1
Hence, Probability of event lies between 0 and 1.
If P(A) = 1, then A is called certain event and A is called an impossible event, if P(A) = 0.
The number of elementary events which will ensures the non-occurrence of A i.e. which ensure the occurrence of A’ is (n – m). Therefore,
P(A’) = \(n – m\over n\)
\(\implies\) P(A’) = 1 – \(m\over n\)
\(\implies\) P(A’) = 1 – P(A)
\(\implies\) P(A) + P(A’) = 1
Also Read : Probability Basic Concepts
Odds in Favour and Against the Occurrence of Event
The odds in favour of occurrence of the event A are defined by m : (n – m) i.e ; P(A) : P(A’)
The odds against the occurrence of A are defined by n – m : m i.e. P(A’) : P(A).
Example : Find the probability of getting a head in a toss of an unbiased coin.
Solution : The sample space associated with the random experiment is S = {H, T}.
\(\therefore\) Total number of elementary events = 2.
We observe that there are two elementary events viz. H, T associated to the given random experiment. Out of these two elementary events only one is favourable i.e. H.
\(\therefore\) Favourable number of elementary events = 1
Hence, Required Probability = \(1\over 2\)
