This the presentation on maths class 11th chapter probability ...... hope you would like it

1. Click to change
the board colour
UNIT IV
PROBABILITY

2. Click to change
the board colour
Definition of Probability:
If there are ‘n’ exhaustive, mutually exclusive and equally likely
outcomes of a random experiment, and ‘m’ of them are
favourable to an event ‘A’, then the probability of happening of ‘A’
is:
where m is no. of favourable events
n is no. of unfavourable events

3. Click to change
the board colour
Terminology Used in Definition:
Random Experiment:
An occurrence which can be repeated a number of times
essentially under the same conditions & whose result can’t
be predicted beforehand, is known as a random
experiment or simply an experiment.
Sample Space & Sample Point:
The set of all possible outcomes of a experiment is called a
sample space (S)
The elements of sample space are called sample points.
A sample space is said to be finite or infinite.
For Eg: If we throw a dice, it can result in any of the six numbers
1,2,3,4,5,6.
Therefore sample space of this experiment is
S= { 1,2,3,4,5,6 } and
n(S) = 6

4. Click to change
the board colour
Event:
Any subset of sample space is called an event.
If S is a sample space, then it is obvious that the null set Ø
and the sample space S it self are events.
For eg: E = { 2,4,6} and n (A) = 3
Exhaustive Outcomes:
By exhaustive we mean that all the possible outcomes have
been taken into consideration and one of them must
happen as a result of an experiment.
For Eg(1): If we throw a dice, there are six exhaustive outcomes ,
namely numbers 1,2,3,4,5,6 coming uppermost.
Eg(2): In tossing a coin there are two exhaustive out comes
namely coming up of head & tail.

5. Click to change
the board colour
Mutually Exclusive Outcomes:
Outcomes are said to be mutually exclusive if the
happening of an outcome excludes the possibility of the
happening of other outcomes.
For e.g.: In tossing a coin, if head coming up then coming up of tail
is excluded in that particular chance.
Equally Likely Outcomes:
Outcomes are said to be equally likely when the
occurrence of none of them is expected in preference to
others.
Independent & Dependent Event:
Two events are said to be independent if the probability of
occurrence of either of them is not affected by the occurrence
or non – occurrence of the other.
On the other hand, if the occurrence of one event affects the
probability of occurrence of the other, then the second event is
said to be dependent on the first.

6. Click to change
the board colour
Illustrations 1:
An unbiased dice is thrown. What is the probability of
i. getting a six
ii. getting either five or six
Solution:
In a single throw of dice, there are six possible outcomes i.e.
1,2,3,4,5,6.
Thus n(S) = 6
i. getting a six
Here n(E) = 1
Therefore required probability:
ii. getting either five or six
Here n(E) = 2
Therefore required probability:

7. Click to change
the board colour
Illustrations 2:
In a simultaneous throw of two die, find the probability of
getting a total of 6.
Solution:
In a simultaneous throw of two die, we have 6 * 6 i.e. 36 possible
outcomes.
Thus n(S) = 36 and
E = { (1,5), (2,4), (3,3), (4,2), (5,1)} i.e. n (E) = 5
Therefore required probability:

14. Click to change
the board colour
THEOREMS OF PROBABILITY:
Addition Theorem (OR Theorem)
Multiplication Theorem (AND Theorem)
Addition Theorem:
Case 1: When events are mutually exclusive:
It state that if two events A & B are mutually exclusive then the
probability of occurrence of either A or B is the sum of the
individual probability of A & B. Symbolically
P(AUB) = P(A) + P(B)
Case 2: When events are NOT mutually exclusive:
It states that if two events A & B are not mutually exclusive, then
probability of the occurrence of either A or B is the sum of the
individual probability of A & B minus the probability of occurrence
of both A and B. Symbolically
P(AUB) = P(A) + P(B) – P(A B)

15. Click to change
the board colour
Conditional Probability:
The probability of occurrence of event A, given that the event B
has already occurred is called conditional probability of
occurrence of A on the condition that B has already occurred.
It is denoted by P(A/B).
If A and B are independent events, then P(A/B) = P(A).
Multiplication Theorem:
The probability of simultaneous occurrence of two events A & B is
the product of probability of A and the conditional probability of B
when A has already occurred or vice – versa. Symbolically
P(A B) = P(A). P(B/A), If P(A) ≠ 0
P(A B) = P(B). P(A/B), If P(B) ≠ 0
It is noted that in case of independent events:
P(A B) = P(A). P(B)