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Probability & Statistics Basics

This document defines key concepts in probability and statistics: 1. It defines probability as the number of favorable outcomes divided by the total number of possible outcomes for an event. It also lists the axioms of probability. 2. Conditional probability is defined as the probability of event B given that event A has occurred. 3. Mean, median and mode are introduced as measures of central tendency, with mean being the average, median being the middle value, and mode being the most frequent value. 4. Standard deviation is defined as a measure of dispersion, calculated as the square root of the variance which is the mean of the squared differences from the mean.

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Ajay Malik
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36 views4 pages

Probability & Statistics Basics

This document defines key concepts in probability and statistics: 1. It defines probability as the number of favorable outcomes divided by the total number of possible outcomes for an event. It also lists the axioms of probability. 2. Conditional probability is defined as the probability of event B given that event A has occurred. 3. Mean, median and mode are introduced as measures of central tendency, with mean being the average, median being the middle value, and mode being the most frequent value. 4. Standard deviation is defined as a measure of dispersion, calculated as the square root of the variance which is the mean of the squared differences from the mean.

Uploaded by

Ajay Malik
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© © All Rights Reserved
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SUB: MATHEMATICS MODULE-13A

MODULE-13A
Definitions of probability and sampling theorems, Conditional
probability, Mean, median, mode and standard deviation
___________________________________________________________________________
Definition of Probability: If the sample space S of an experiment consists of finitely many
outcomes (points) that are equally likely, then the probability P (A) of an event A is

( )

Thus, in particular ( )

Given a sample S, with each event A of S, there is associated a number P (A), called
the probability of A, such that the following axioms of probability are satisfied.

1. For every A is S ( )
2. The entire sample space S has the probability
( )

3. For mutually exclusive events A & B ( )


( ) ( ) ( )

4. For an event A and its complement in a sample space S,


( ) ( )
5. For mutually exclusive events sample space S,
( ) ( ) ( ) ( )
6. For events A and B in a sample space

( ) ( ) ( ) ( )

JH ACADEMY Page 1
SUB: MATHEMATICS MODULE-13A

Conditional Probability:
Often it is required to find the probability of an event B under the condition that an
event A occurs. This probability is called the conditional probability of B given A and is
denoted by ( ⁄ )
( )
( ⁄ ) P (A)
( )

( )
Similarly ( ⁄ ) P (B)
( )

Multiplication Rule:
If A and B are events in a sample space S and P (A) , P (B) , then

( ) ( ) ( ⁄ ) ( ) ( ⁄ )

Permutations:
A permutation of given things is an arrangements of these things in a row in some
order. The number of different permutations of ‘n’ different things taken ‘k’ at a time without
repetitions is ( )
and with repetitions is .

Combinations:
In permutation, the order of the selected things is essential. In contrast, a combination
of given things means any selection of one or more things without regard to order.
The number of combinations of ‘n’ different things taken ‘k’ at a time, without
repetitions is ( )
and the number of these combinations with repetition is

( )
( )

1. Mean:
If are set of n values of variate, then the arithmetic
Mean (or simply mean) is given by

∑
̅

In a frequency distribution, if be the mid values of the class


intervals having frequencies respectively, we have

∑
̅
∑

JH ACADEMY Page 2
SUB: MATHEMATICS MODULE-13A

2. Median:
If the values of a variable are arranged in the ascending order of magnitude,
the median is the middle item if the number is odd and is the mean of the two middle
items if the number is even. Thus the median is equal to the mid value. i.e. the value
which divides the total frequency into two equal parts.

L m

3. Mode:
The mode is defined as that value of the variable which occurs most frequently i.e. the
value of the maximum frequency.

JH ACADEMY Page 3
SUB: MATHEMATICS MODULE-13A

( )

( )

[ ] [ ]

( )

4. Standard deviation:

The most important measure of dispersion is the standard deviation. It is


denoted by . It is computed as the square root of the mean of the square of the
differences of the variable values from their mean.

∑ ( )
√

The square of standard deviation is known as variance.

JH ACADEMY Page 4

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