Probability
Probability
Probability is just the chance of happening of an event . In other words , Probability is a branch of mathematics that deals with calculating the likelihood of a given event's occurrence which is expressed as a number between 1 and 0.
e.g. The probability of a coin toss resulting in head is 1/2. The probability is defined as the chance of happening or not happening of an event.
Important terms Related to probability :
* Experiment An action which result in some well-defined outcomes .
* Random experiment A random experiment is an experiment or a process for which the outcomes cannot be predicted with certainity .
Whenever an experiment is conducted a number of times under similar condition where the resultis not certain , then the experiment is called a trial or a random experiment , the outcomes are known as events.
e.g. When a die is thrown , it is a trial , getting a number 1 or 2 or 3 or 4 or 5 or 6 is an event.
* Sample Space A sample space of an experiment is the set of all possible outcomes of that experiment. It is denoted by S.
e.g. If is a throw a die, then sample space , S = {1,2,3,4,5,6}
* Event It is a single result of an experiment .
* Equally likely events : Events are said to be equally likely when they have an equal probability of occurrence.
e.g. When a die is thrown any number 1 or 2 or 3 or 4 or 5 or 6 may occur. In this trial , the six events are equally likely.
*Exhaustive Events : A set of events is said to be exhaustive , if one of them must necessarily happen every time the experiment is performed .
e.g. When a die id thrown , there are six exhaustive events.
* Mutually exclusive events : If the occurrence of anyone of the events in a trial prevents the others then the events are said to be mutually exclusive events.
e.g. When a die is thrown , the event of getting faces numbered 1 to 6 are mutually exclusive events.
e.g. When a die is thrown , it is a trial , getting a number 1 or 2 or 3 or 4 or 5 or 6 is an event.
* Sample Space A sample space of an experiment is the set of all possible outcomes of that experiment. It is denoted by S.
e.g. If is a throw a die, then sample space , S = {1,2,3,4,5,6}
* Event It is a single result of an experiment .
* Equally likely events : Events are said to be equally likely when they have an equal probability of occurrence.
e.g. When a die is thrown any number 1 or 2 or 3 or 4 or 5 or 6 may occur. In this trial , the six events are equally likely.
*Exhaustive Events : A set of events is said to be exhaustive , if one of them must necessarily happen every time the experiment is performed .
e.g. When a die id thrown , there are six exhaustive events.
* Mutually exclusive events : If the occurrence of anyone of the events in a trial prevents the others then the events are said to be mutually exclusive events.
e.g. When a die is thrown , the event of getting faces numbered 1 to 6 are mutually exclusive events.
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