Many events can't be predicted with total certainty. The best we can say is how
likely they are to happen, using the idea of probability.
Terminology of Probability Theory
Experiment: A trial or an operation conducted to produce an outcome is called an
experiment.
Sample Space: All the possible outcomes of an experiment together constitute a
sample space. For example, the sample space of tossing a coin is {head, tail}.
Favorable Outcome: An event that has produced the desired result or expected
event is called a favorable outcome. For example, when we roll two dice, the
possible/favorable outcomes of getting the sum of numbers on the two dice as 4
are (1,3), (2,2), and (3,1).
Trial: A trial denotes doing a random experiment.
Event: The total number of outcomes of a random experiment is called an event.
Exhaustive Events: When the set of all outcomes of an event is equal to the
sample space, we call it an exhaustive event.
***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.
**P(E) = n(E)/n(S)
**E’ represents that the event will not occur.
Therefore, now we can also conclude that, P(E) + P(E’) = 1
The number of favorable outcomes :m
The number of possible outcomes:n
P(A)=
m
n
