Meaning and definition of Probability
As the Oxford dictionary states it, Probability means ‘The extent to which something is probable; the likelihood of something happening or being the case’.
In mathematics too, probability indicates the same – the likelihood of the occurrence of an event.
Basic formula of probability
The Probability of the occurrence of an event A is defined as:
P(A) = (No. of ways A can occur)/(Total no. of possible outcomes)
Compound probability
Compound probability is when the problem statement asks for the likelihood of the occurrence of more than one outcome.
Formula for compound probability
P(A or B) = P(A) + P(B) – P(A and B)
Experiment:
An operation which can produce some well-defined outcomes is called an experiment.
Random Experiment:
An experiment in which all possible outcomes are know and the exact output cannot be predicted in advance, is called a random experiment.
Mutually exclusive events:
Mutually exclusive events are those where the occurrence of one indicates the non-occurrence of the other
OR
When two events cannot occur at the same time, they are considered mutually exclusive.
Sample Space
Sample Space is the set of all possible outcomes of an experiment. It is denoted by S.
Examples
i) When a coin is tossed, S = {H, T} where H = Head and T = Tail
ii) When a dice is thrown, S = {1, 2 , 3, 4, 5, 6}
iii) When two coins are tossed, S = {HH, HT, TH, TT} where H = Head and T = Tail
Event
Any subset of a Sample Space is an event. Events are generally denoted by capital letters A, B , C, D etc.
Examples
i) When a coin is tossed, outcome of getting head or tail is an event
ii) When a die is rolled, outcome of getting 1 or 2 or 3 or 4 or 5 or 6 is an event