In an experiment, the probability of an event is the possibility of that event occurring. The probability of any event is a value between (and including) “0” and “1”.
Events in Probability
In probability theory, an event is a set of outcomes of an experiment or a subset of the sample space.
If P(E) represents the probability of an event E, then, we have,
- P(E) = 0 if and only if E is an impossible event.
- P(E) = 1 if and only if E is a certain event.
- 0 ≤ P(E) ≤ 1.
Suppose, we are given two events, “A” and “B”, then the probability of event A, P(A) > P(B) if and only if event “A” is more likely to occur than the event “B”. Sample space(S) is the set of all of the possible outcomes of an experiment and n(S) represents the number of outcomes in the sample space.
P(E) = n(E)/n(S)
P(E’) = (n(S) – n(E))/n(S) = 1 – (n(E)/n(S))
E’ represents that the event will not occur.
Therefore, now we can also conclude that, P(E) + P(E’) = 1