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.

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.