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Definition

Probability is a numerical measure which indicates the chance of occurrence of an event.

 

It is a number which ranges from 0 to 1.

 

If the probability of occurrence of an event is zero, then it means that the event cannot occur at all and if the probability is 1, then it means that the event is certain to occur.

Important Terms Used in Probability

  • Random experiment: An experiment is an activity that produces a number of results or outcomes. An experiment can be repeated under similar conditions for a finite number of times and can result in any one of the several possible outcomes. It may not result in the same outcome when repeated under the same conditions.
     
    Random experiment is an experiment which does not have a unique outcome.
  • Sample space: A set of all possible outcomes of a random experiment is called sample space. Usually it is denoted by S or U. The outcomes of the random experiment are called sample points or outcomes or cases.
  • Events: The results or outcomes of a random experiment are known as events.
  • Simple event: An event which cannot be decomposed into further events is known as simple event.
  • Composite event: Composite events are those events that can be decomposed into two or more simple events.
  • Complementary events: If U is a finite sample space and A is any event of U, then the set of elements which are in U, but not in A is called complementary event of A denoted by A′ or AC.„
  • Impossible event: An event which can never occur when a certain random experiment is performed is called an impossible event.
  • Union of two events: If U is a finite sample space and A and B are any two events of it, then the set of all elements of A and B is called the union of two events and is denoted by A  B.
  • Intersection of two events: If A and B are any two events of the sample space U, then the set of elements which are common to both A and B, is called intersection of two events and is denoted by A  B.
  • Difference events: If A and B are any two events of the sample space U, then the set of the elements which are in A but not in B is called a difference event which is denoted by A – B or A  B.
  • Exhaustive events: A set of events is exhaustive if any one event of the events in the set has to occur whenever the experiment is conducted.
     
    The union of all the exhaustive events is equal to the sample space.
  • Mutually exclusive events: Events are said to be mutually exclusive if occurrence of one event rules out the possibility of the other. Their intersection event is the null set, i.e., the events are said to be mutually exclusive if they do not occur together or the occurrence of one event resists the occurrence of other events.
  • Mutually independent events: If the occurrence of one event does not depend on the occurrence or non-occurrence of other events, then the events are said to be mutually independent.
  • Equally likely events: Events are said to be equally likely, if they have same chances of occurrence.

Note: If A ⊂ B, then
(i) P(B – A) = P(B) – P(A)
(ii) P(B) ≥ P(A)





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