Introduction to Probability Theory, Schemes and Mind Maps of Statistics

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Probability Theory

for lecturer mathematics

0301 - 4889903

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 Some basic terminologies

 Sample Space

Experiment: Any process of observations is called experiment. Outcomes: The result of an observation are known as outcomes of an experiment. Random Experiment: An experiment is called a random experiment if its outcomes cannot be predicted. So a random experiment is an experiment which produces different outcomes even if it is repeated a large number of times under similar conditions. Examples:

1. Rolling a die.
2. Tossing a coin.
3. Drawing a card from a deck.
4. Choosing a ball from a bag containing balls of different colors. Sample Space: The set of all possible outcomes of a random experiment is called sample space. Denoted by S. An element of S is called a sample point.

4. In tossing four coins. ( 2 4 = 16 ) 𝐻 𝐻 𝐻 𝐻 𝑇 𝑇 𝑇 𝑇 𝐻 𝐻 𝐻 𝐻 𝑇 𝑇 𝑇 𝑇 𝐻 𝐻 𝑇 𝑇 𝐻 𝐻 𝑇 𝑇 𝐻 𝐻 𝑇 𝑇 𝐻 𝐻 𝑇 𝑇 𝐻 𝑇 𝐻 𝑇 𝐻 𝑇 𝐻 𝑇 𝐻 𝑇 𝐻 𝑇 𝐻 𝑇 𝐻 𝑇 𝐻 𝐻 𝐻 𝐻 𝐻 𝐻 𝐻 𝐻 𝑇 𝑇 𝑇 𝑇 𝑇 𝑇 𝑇 𝑇

4. In rolling a die. Sample space is given by ( 6 1 = 6 )
5. In rolling two dice. Sample space is given by ( 6 2 = 36 ) 𝑆 = { 1 , 2 , 3 , 4 , 5 , 6 } 𝑆 = { ( 1 , 1 ), ( 1 , 2 ), ( 1 , 3 ), ( 1 , 4 ), ( 1 , 5 ), 1 , 6 , 2 , 1 , 2 , 2 , 2 , 3 , 2 , 4 , ( 2 , 5 ), 2 , 6 , 3 , 1 , 3 , 2 , 3 , 3 , 3 , 4 , 3 , 5 , 3 , 6 , 4 , 1 , 4 , 2 , 4 , 3 , 4 , 4 , 4 , 5 , 4 , 6 , 5 , 1 , 5 , 2 , 5 , 3 , 5 , 4 , 5 , 5 , 5 , 6 , ( 6 , 1 ), ( 6 , 2 ), ( 6 , 3 ), ( 6 , 4 ), ( 6 , 5 ), 6 , 6 }

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