Sample Space
Sample Space is the set of all possible outcomes of an experiment. It is denoted by S.
Sample Space is the set of all possible outcomes of an experiment. It is denoted by S.
Examples
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When a coin is tossed, S = {H, T} where H = Head and T = Tail
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When a dice is thrown, S = {1, 2 , 3, 4, 5, 6}
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When two coins are tossed, S = {HH, HT, TH, TT} where H = Head and T = Tail
Event
Any subset of a Sample Space is an event. Events are generally denoted by capital letters A, B , C, D etc.
Examples
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When a coin is tossed, outcome of getting head or tail is an event
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When a die is rolled, outcome of getting 1 or 2 or 3 or 4 or 5 or 6 is an event
Examples
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When a coin is tossed, outcome of getting head or tail is an event
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When a die is rolled, outcome of getting 1 or 2 or 3 or 4 or 5 or 6 is an event
Equally Likely Events
Events are said to be equally likely if there is no preference for a particular event over the other.
Examples
When a coin is tossed, Head (H) or Tail is equally likely to occur.
When a dice is thrown, all the six faces (1, 2, 3, 4, 5, 6) are equally likely to occur.
Mutually Exclusive Events
Two or more than two events are said to be mutually exclusive if the occurrence of one of the events excludes the occurrence of the other
This can be better illustrated with the following examples
Note : If A and B are mutually exclusive events, A ∩ B = ϕ where ϕ represents empty set.
When a coin is tossed, we get either Head or Tail. Head and Tail cannot come simultaneously. Hence occurrence of Head and Tail are mutually exclusive events.
When a die is rolled, we get 1 or 2 or 3 or 4 or 5 or 6. All these faces cannot come simultaneously. Hence occurrences of particular faces when rolling a die are mutually exclusive events.
Consider a die is thrown and A be the event of getting 2 or 4 or 6 and B be the event of getting 4 or 5 or 6. Then
A = {2, 4, 6} and B = {4, 5, 6}
Here A ∩ B ≠ϕ. Hence A and B are not mutually exclusive events.
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