Introduction to Probability

Probability is that branch of Mathematics which deals with the measure of uncertainty in various phenomenon that gives several results or outcomes instead of a particular one.

Definition of probability: Numerical measure of Uncertainty and denoted by P(E).

Experiment: An activity which produces some well defined outcomes.

Random Experiment: An experiment in which all possible outcomes are known but the results can not be predicted in advance.

Trial: Performing an experiment.

Outcome: Result of the trial.

Equally likely outcomes: Outcomes which have equal chances of occurrence.

Sample space: Collection of all possible outcomes.

Coin tossed once: S = {H, T}

Coin tossed twice: S = {HH, HT, TH, TT}

Die is thrown once: S = {1, 2, 3, 4, 5, 6}

Event: Collection of some including no outcome or all outcomes from the sample space.

Probability of an event:

$$ \text{P(E)} = \frac{\text{Number of outcomes favourable to E}}{\text{Number of all possible outcomes of experiment}} $$

Sure Event: If number of outcomes favourable to the event is equal to number of total outcomes of the sample space or an event whose probability is 1.

Impossible Event: Having no outcome or an event whose probability is 0.

Range of Probability: Probability of an event always lies between 0 and 1 (0 and 1 inclusive).

0 ≤ P(E) ≤ 1

Complementary Event: Event which occurs only when E does not occur.

P(E') = 1 - P(E)

Sum of Probabilities: Sum of all the probabilities is 1.