Define :
(1) Random Experiment
(2) Sample Space
(3) Equi-probable Events
(4) Favourable Outcomes
(5) Probability (Mathematical definition)
(6) Probability (Statistical definition)
(7) Impossible Event
(8) Certain Event

Question

Define :

(1) Random Experiment

(2) Sample Space

(3) Equi-probable Events

(4) Favourable Outcomes

(5) Probability (Mathematical definition)

(6) Probability (Statistical definition)

(7) Impossible Event

(8) Certain Event

Accepted Answer

(1) Random Experiment: An experiment that can be independently repeated under identical conditions, all possible outcomes are known, but which outcome will appear cannot be predicted with certainty. (2) Sample Space: The set of all possible outcomes of a random experiment, denoted by U or S. (3) Equi-probable Events: Events for which there is no apparent reason to believe that any one event is more or less likely to occur than the others. (4) Favourable Outcomes: The outcomes out of all elementary outcomes in the sample space that indicate the occurrence of a certain event A. (5) Mathematical/Classical Definition: If n outcomes are mutually exclusive, exhaustive and equi-probable and m are favourable for event A, then P(A) = m/n. (6) Statistical Definition: If an experiment is repeated n times and event A occurs m times, then P(A) = lim(n→∞) m/n, the limiting relative frequency. (7) Impossible Event: The special subset φ of the sample space that never occurs; P(φ) = 0. (8) Certain Event: The special subset U of the sample space that always occurs; P(U) = 1.