Flashcards: Probability | Flashcards for JEE PDF Download

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PROBABILITY 
Probability or chance is a measure of uncertainty in any event occurring. Life if full of uncertainties. 
Probability measures the degree of uncertainty between 0 and 1 . 
Galileo was first to attempt probability while he was dealing with some problem relating to dice in 
gambling. The foundation of theory of probability was laid by B. Pascal and P. Fermat. Now probability is 
widely used in business and economics for making future predictions. 
  
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PROBABILITY 
Probability or chance is a measure of uncertainty in any event occurring. Life if full of uncertainties. 
Probability measures the degree of uncertainty between 0 and 1 . 
Galileo was first to attempt probability while he was dealing with some problem relating to dice in 
gambling. The foundation of theory of probability was laid by B. Pascal and P. Fermat. Now probability is 
widely used in business and economics for making future predictions. 
  
 
 
 
 
 
Experimental or trial 
An operation which results in some well defined outcomes. 
Random Experiment 
An experiment whose outcome cannot be predicted with certainty is called a random experiment. 
Tossing of a coin is a random experiment. 
Throwing a die is a random experiment. 
  
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PROBABILITY 
Probability or chance is a measure of uncertainty in any event occurring. Life if full of uncertainties. 
Probability measures the degree of uncertainty between 0 and 1 . 
Galileo was first to attempt probability while he was dealing with some problem relating to dice in 
gambling. The foundation of theory of probability was laid by B. Pascal and P. Fermat. Now probability is 
widely used in business and economics for making future predictions. 
  
 
 
 
 
 
Experimental or trial 
An operation which results in some well defined outcomes. 
Random Experiment 
An experiment whose outcome cannot be predicted with certainty is called a random experiment. 
Tossing of a coin is a random experiment. 
Throwing a die is a random experiment. 
  
 
 
 
 
 
Sample Space 
The set of all possible outcomes of an experiment is called the sample space of that experiment. 
It is denoted by ?? . 
When a coin is tossed the sample space ?? = {?? , ?? } 
When a die is thrown, the sample space ?? = {1,2,3,4,5,6} 
  
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PROBABILITY 
Probability or chance is a measure of uncertainty in any event occurring. Life if full of uncertainties. 
Probability measures the degree of uncertainty between 0 and 1 . 
Galileo was first to attempt probability while he was dealing with some problem relating to dice in 
gambling. The foundation of theory of probability was laid by B. Pascal and P. Fermat. Now probability is 
widely used in business and economics for making future predictions. 
  
 
 
 
 
 
Experimental or trial 
An operation which results in some well defined outcomes. 
Random Experiment 
An experiment whose outcome cannot be predicted with certainty is called a random experiment. 
Tossing of a coin is a random experiment. 
Throwing a die is a random experiment. 
  
 
 
 
 
 
Sample Space 
The set of all possible outcomes of an experiment is called the sample space of that experiment. 
It is denoted by ?? . 
When a coin is tossed the sample space ?? = {?? , ?? } 
When a die is thrown, the sample space ?? = {1,2,3,4,5,6} 
  
 
 
 
 
 
EVENT 
A subset of the sample is called an event. 
Types of events 
Simple event or elementary event : 
An event is called a simple event, if it is a singleton subset of the sample space ?? . 
For example, getting of three heads in a simultaneous throw of 3 coins in a simple event. 
  
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PROBABILITY 
Probability or chance is a measure of uncertainty in any event occurring. Life if full of uncertainties. 
Probability measures the degree of uncertainty between 0 and 1 . 
Galileo was first to attempt probability while he was dealing with some problem relating to dice in 
gambling. The foundation of theory of probability was laid by B. Pascal and P. Fermat. Now probability is 
widely used in business and economics for making future predictions. 
  
 
 
 
 
 
Experimental or trial 
An operation which results in some well defined outcomes. 
Random Experiment 
An experiment whose outcome cannot be predicted with certainty is called a random experiment. 
Tossing of a coin is a random experiment. 
Throwing a die is a random experiment. 
  
 
 
 
 
 
Sample Space 
The set of all possible outcomes of an experiment is called the sample space of that experiment. 
It is denoted by ?? . 
When a coin is tossed the sample space ?? = {?? , ?? } 
When a die is thrown, the sample space ?? = {1,2,3,4,5,6} 
  
 
 
 
 
 
EVENT 
A subset of the sample is called an event. 
Types of events 
Simple event or elementary event : 
An event is called a simple event, if it is a singleton subset of the sample space ?? . 
For example, getting of three heads in a simultaneous throw of 3 coins in a simple event. 
  
 
 
 
Mixed event or compound event : 
A subset of the sample space ?? which contains more than one element is called a mixed event. For 
example, getting the same number on both die, when cast together is a compound event.