# Probability

## Probability is measure of uncertainty on a scale. An action (or operation) which results in some (well-defined) outcomes is called an experiment. An experiment is called random experiment if it results in two or more outcomes and it is not possible to tell (predict) the outcome in advance. The collection of all possible outcomes of a random experiment is called sample space associated with it. It is usually denoted by S. Each element of the sample space is called a sample point. A subset of the sample space associated with a random experiment is called an event. When the outcome of an experiment satisfies the condition mentioned in the event, then we say that event has occurred. The theoretical probability or the classical probability of an event E, written as P(E), is defined as : P(E) = (Number of outcomes favourable to E)/ (Total number of all possible outcomes of the experiment). In this approach, for a given sample space, probability is considered as a function which assigns a non-negative real number P(A) to every event A. This approach of probability is based upon certain axioms. Types of Events: • Simple events • Compound events • Sure events • Impossible events Algebra of Events: • Complementary events • The event ‘A or B’ • The event ‘A and B’ • The event ‘A but not B’ • Mutually exclusive events • Exhaustive events Keywords: Impossible and sure event, complementary event or ‘not event’, mutually exclusive events, exhaustive and mutually exclusive events.

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