presentation for probability with good explanations and examples

1. Presentation by-

2. What is probability
> Probability is the chance or the likelihood
Of the happening of some event.
> Or we can say that , it is possibility of
happening of an event.
Kunal

3. Examples of probabilty
It may rain or may not rain today.
When a die Is thrown it may turn up a particular number
4 or not .
It may turn up anyone of the numbers 1,2,3,4,5,6 but not
sure that which number will appear.
Kunal

4. Random experiment
An experiment whose outcome can’t be
predicted in advance is k/a Random experiment.
For example:
throwing an unbiased coin is a random
experiment because when a coin is tossed we
ca’t say with surety that either a head or a tail will
come although the possibility of appearance of
head or tail is equally probable.
Kunal

5. Sample space
The set of all possible results or outcomes of an experiment is called
sample space .
For example if we toss a coin , there are two possible results ,
namely a head or a tail .
So the sample space in this experiment is head or tail i.e. n(s)=2.
Kunal

6. Types of event
Any subset of a sample space is called an event.
there are various type of events , some of which are :-
> Simple event – An event having only one sample point is
called simple event.
for ex: when we throw a die then any one of the numbers
from 1 to 6 may appear. Then appearance of any of the single
number will come under simple event.
> Compound event – A subset of sample space which has
more than one sample point is called compound event.
for example: when two coins are tossed then the sample
space will be {HH,HT,TH,TT} ,then the event of getting atleast one
head is a compound event.
Kunal

7. Equally likely events : when the chances of happening of an
event is not greater than or less than those of any other event oof the
same sample space.
for example :
when a die is thrown then all the six faces i.e. 1,2,3,4,5,6 is equally
likely to come up. There is no reason to expect any specific number
to appear.
Kunal

8. Mutually exclusive event:
If we roll an unbiased die, then we shall get either an odd number or
an even number.
Let A = the event of getting an odd number and B = the event of
getting an even number.
Obviously the two events cannot occur simultaneously .in fact, the
occurrence of A excludes the occurrence of B. we call such events as
mutually exclusive events.
Kunal

9. Exhaustive and mutually exclusive events
A set of events is said to be exhaustive and mutually exclusive
If the events are exhaustive as well as mutually exclusive.
Thus it is said to be exhaustive and mutually exclusive event if the
union of all the events results the sample space.
And intersection of two events gives no value i.e. fi.
For example:
Let A={1,3,5}=the event of occurrence of odd numbers.
And B={2,4,6}=the event of occurrence of even numbers.
Then obviously here,
A U B ={1,2,3,4,5,6} and AnB={fi}
Thus AUB=S and AnB=fi.
Hence, A and B are exhaustive and mutually exclusive events.
Kunal

10. Exhaustive and mutually exclusive events
A set of events is said to be exhaustive and mutually exclusive
If the events are exhaustive as well as mutually exclusive.
Thus it is said to be exhaustive and mutually exclusive event if the
union of all the events results the sample space.
And intersection of two events gives no value i.e. fi.
For example:
Let A={1,3,5}=the event of occurrence of odd numbers.
And B={2,4,6}=the event of occurrence of even numbers.
Then obviously here,
A U B ={1,2,3,4,5,6} and AnB={fi}
Thus AUB=S and AnB=fi.
Hence, A and B are exhaustive and mutually exclusive events.
Kunal

11. Probability of an event
Probability of an event is calculated by dividing
the number of favorable outcomes to the given
event w.r.t. the total no outcomes.
for example :
Probability of getting 4 is 1/6 when a die is tossed
because here number of outcomes favorable to
event is 1 i.e. the number 4 and the total number
of outcomes is 6.
Kunal

12. Thank you
Kunal