Basics of Probability:
Sample Space:
- The set of all possible outcomes in a random experiment.
- It is denoted by S.
Sample Point:
- Each outcome of the set or every element of the set.
Let see an example:
If a coin is tossed then the Sample Space is: S = { H, T} , where H - Head, T - Tail are Sample Points.
Event:
- Every non-empty subset of Sample Space.
- A ∪ B is the event "either A or B or both".
- A ∩ B is the event "both A and B".
- A' is the event "not A". A' is the complement of A.
- A - B is the event "A but not B".
Event:
- Every non-empty subset of Sample Space.
- A ∪ B is the event "either A or B or both".
- A ∩ B is the event "both A and B".
- A' is the event "not A". A' is the complement of A.
- A - B is the event "A but not B".
Types of Events:
Simple or Elementary Event:
- In such events the Sample Space contains only one element.
Example:
If a dice is thrown and number 5 comes on its upper surface then it is the simple element expressed as { 5 }.
Composite Event:
- In this event the number of elements in the Sample Space is more than one.
Example:
If a dice A thrown and even number appears on dice, A = { 2, 4, 6 } is the composite event.
Sure and Certain Events:
- If S is a Sample Space in a random experiment, then since S ⊆ S i.e. S is a subset of itself, hence S is a same event.
Example:
If a coin is tossed then getting Head or Tail is same event.
Impossible Event:
- If there is no element in Sample Space corresponding to an event, then it is an impossible event.
Equally Likely Event:
- In this all the events have equal preference.
Compound or Mixed Events:
- If happens two or more than two events is related to each other then event of two happens together is called a compound event.
Independent Events:
- Two events A and B are said to be independent events, if the occurrence of one does not depend upon occurrence of another.
Exhaustive Events:
Total number of possible outcomes.
Independent Events:
- Two events A and B are said to be independent events, if the occurrence of one does not depend upon occurrence of another.
Exhaustive Events:
Total number of possible outcomes.
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