Notes On Probability - Theoretical Approach - CBSE Class 10 Maths
In general life there are some words likely, may be, probably, chance, hope, it may possible e.t.c. All these are synonyms to probability. Probability is a quantitative measure of certainty. Random Experiment Any activity which is associated to certain outcome is called random experiment. e.g. tossing a coin, throwing a die. Experimental or Empirical probability: The probability that is based on the observations of an experiment is called an experimental or empirical probability. As the number of observations in an experiment increases, the experimental probability gets closer to the theoretical probability. The results of an experiment are called outcomes. Elementary events: The possible outcomes of an experiment are called its elementary events. The sum of the probabilities of elementary events of an experiment is one. These outcomes are said to be equally likely if each outcome has the same chance of happening. Complementary events: Events that are mutually exclusive of each other are called complementary events. The sum of the probabilities of two complementary events is always equal to one. Impossible event: An event having zero probability of occurrence is called an impossible event. Sure or Certain event: An event having a probability of 1 is called a sure or certain event. An event E is a number P(E), such that 0 ≤ P(E) ≤ 1. Compound event An event associated to a random experiment is a compound event if it is obtained by combining two or more elementary events associated to the random experiment. Occurrence of an event An event A associated to a random experiment is said to be occur if any one of the elementary events associated to the event A is an outcome. Negation of an event Corresponding to every event A associated with a random experiment, an event "not A" which occurs when and only when A does not occur. The event "not A" is called the negation of event A and is denoted as $\stackrel{\text{_}}{\text{A}}$. The theoretical or classical probability of an event E is denoted by P(E), where P( E) = $\frac{\text{Number of outcomes favorable to E}}{\text{Total number of possible out comes}}$.

#### Summary

In general life there are some words likely, may be, probably, chance, hope, it may possible e.t.c. All these are synonyms to probability. Probability is a quantitative measure of certainty. Random Experiment Any activity which is associated to certain outcome is called random experiment. e.g. tossing a coin, throwing a die. Experimental or Empirical probability: The probability that is based on the observations of an experiment is called an experimental or empirical probability. As the number of observations in an experiment increases, the experimental probability gets closer to the theoretical probability. The results of an experiment are called outcomes. Elementary events: The possible outcomes of an experiment are called its elementary events. The sum of the probabilities of elementary events of an experiment is one. These outcomes are said to be equally likely if each outcome has the same chance of happening. Complementary events: Events that are mutually exclusive of each other are called complementary events. The sum of the probabilities of two complementary events is always equal to one. Impossible event: An event having zero probability of occurrence is called an impossible event. Sure or Certain event: An event having a probability of 1 is called a sure or certain event. An event E is a number P(E), such that 0 ≤ P(E) ≤ 1. Compound event An event associated to a random experiment is a compound event if it is obtained by combining two or more elementary events associated to the random experiment. Occurrence of an event An event A associated to a random experiment is said to be occur if any one of the elementary events associated to the event A is an outcome. Negation of an event Corresponding to every event A associated with a random experiment, an event "not A" which occurs when and only when A does not occur. The event "not A" is called the negation of event A and is denoted as $\stackrel{\text{_}}{\text{A}}$. The theoretical or classical probability of an event E is denoted by P(E), where P( E) = $\frac{\text{Number of outcomes favorable to E}}{\text{Total number of possible out comes}}$.