Probability Definition : The probability of a given event is an expression of likelihood of occurrence of an event.A probability isa number which ranges.

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Presentation transcript:

Probability Definition : The probability of a given event is an expression of likelihood of occurrence of an event.A probability isa number which ranges from 0 to 1. 0 for an event which cannot occur 1 for an event which can occur

Importance for the concept of Probability According to Ya-lun Chou : “Statistics as a method of decision- making under uncertainty, is founded on probability theory, since probability is at once the language and the measure of uncertainty and the risks associated with it.”

Experiment : The term experiment refers to processes which result in different possible outcomes or observations. Random Experiment : 1) all possible outcomes are known in advance. 2) none of the outcomes can be predicted with certainty.

Note : Each performance of a random experiment is called a Trial and the result of a performance ( or trial) is called an outcome or case. Sample Point : The outcome of the random experiment is called a sample point. Sample space : The set of all possible outcomes ( or sample points) of a random experiment is called a sample space.

Finite Sample space : A sample space is said to be finite if it contains a finite number of sample points. Infinite Sample space : A sample space is said to be infinite if it contains a infinite number of sample points. Discrete Sample space: A sample space is said to be discrete if it contains finite or finitely many or countably infinite sample points which can be arranged into a simple sequence E1,E2…….. Corresponding to natural number.

Continuous Sample space : A sample space is said to be continuous if it contains non-denumerable(uncountable) number of sample points. Events: A subset of a sample space is called an event. An empty subset φ of S us called impossible event and the space itself is called a certain event. The subset containing a simple sample point is known as simple event or elementary event.

Types of event Equally like Events : Two or more events are said to be equally likely if any one of them can not be expected to occur in preference to the others. Example: In a tossing of an unbiased coin, Head is likely to come up as tail. Composite Event : The union of two events A & B denoted by A U B and A + B is called a composite event of A & B.

Compound Event: The intersection of two events A & B denoted by A∩B or AB is called compound event of A & B. Mutually Exclusive ( or Incompatible) Events : Two events are said to be mutually exclusive if they have no sample point in common i.e. A∩B=Ф Exhaustive events : Two events are exhaustive if their union is equal to the sample space. Independent Events: Two or more events are said to be independent if the occurrence of one does not affect the occurrence of the other.

Dependent Events : Two events are said to be dependent if the occurrence of one affects the occurrence of the other. Mutually exclusive & Exhaustive Events : A number of events are said to be mutually exclusive & exhaustive events if i) every two of them are mutually exclusive ii)one of them necessarily occurs in any trial.