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.

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. For example,

  • Coin tossed once: S = {H, T}
  • Coin tossed twice or two coins tossed simultaneously: 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: Number of outcomes favourable to the event divided by total number of outcomes in the sample space.

P(E) = n(E)/n(S)

Sure Event: 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.