Probability terminologies
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This document defines key concepts related to random experiments and probability. It explains that a random experiment is an experiment that can be repeated under the same conditions and has outcomes that can be counted. The set of all possible outcomes is called the sample space. Events are subsets of outcomes that meet specified conditions. There are different types of events including elementary events containing a single outcome, composite events with multiple outcomes, and mutually exclusive events where the occurrence of one prevents others. The document also defines concepts such as exhaustive events, favorable events, independent events, and dependent events.
![The set of all possible outcomes of a random
experiment is known as “Sample Space” and
denoted by set S. [this is similar to Universal
set in Set Theory] The outcomes of the
random experiment are called sample points
or outcomes.](https://image.slidesharecdn.com/probabilityterminologies-200117164859/85/Probability-terminologies-3-320.jpg)
Probability terminologies
- 1. By Dr. Satyanarayan Pandey Department of Management Studies BBMKU, Dhanbad
- 2. If an experiment or trial is repeated under the same conditions for any number of times and it is possible to count the total number of outcomes is called as “Random Experiment”.
- 3. The set of all possible outcomes of a random experiment is known as “Sample Space” and denoted by set S. [this is similar to Universal set in Set Theory] The outcomes of the random experiment are called sample points or outcomes.
- 4. An „event‟ is an outcome of a trial meeting a specified set of conditions other words, event is a subset of the sample space S. Events are usually denoted by capital letters. There are different types of events. 1. Null or impossible event is an event which contains no outcomes. 2. Elementary event is an event which contains only one outcomes. 3. Composite event is an event which contains two or more outcomes. 4. Sure or certain event is an event which contains all the outcomes of a sample space.
- 5. 5. Exhaustive Events: The total number of all possible elementary outcomes in a random experiment is known as „exhaustive events‟. In other words, a set is said to be exhaustive, when no other possibilities exists. 6. Favourable Events: The elementary outcomes which entail or favour the happening of an event is known as „favourable events‟ i.e., the outcomes which help in the occurrence of that event. 7. Mutually Exclusive Events: Events are said to be „mutually exclusive‟ if the occurrence of an event totally prevents occurrence of all other events in a trial. In other words, two events A and B cannot occur simultaneously.
- 6. 8. Equally likely or Equi-probable Events: Outcomes are said to be ‘equally likely’ if there is no reason to expect one outcome to occur in preference to another. i.e., among all exhaustive outcomes, each of them has equal chance of occurrence. 9. Complementary Events: Let E denote occurrence of event. The complement of E denotes the non occurrence of event E. Complement of E is denoted by ‘Ē’. 10. Independent Events: Two or more events are said to be ‘independent’, in a series of a trials if the outcome of one event is does not affect the outcome of the other event or vise versa. 11. Dependent events : In other words, several events are said to be „dependents‟ if the occurrence of an event is affected by the occurrence of any number of remaining events, in a series of trials. Measurement of Probability.