CBSE Class 12 > Class 12 Videos > Partition Sample Space, Total Probability Theorem (Part - 17) - Probability, Maths, Class 12
Partition Sample Space, Total Probability Theorem (Part - 17) - Probability,
FAQs on Partition Sample Space, Total Probability Theorem (Part - 17) - Probability, Maths, Class 12
| 1. What is the sample space in probability? |  |
Ans. The sample space in probability refers to the set of all possible outcomes of a random experiment. It is denoted as "S" and can be represented using a list, set, or a tree diagram. Each outcome in the sample space has a certain probability associated with it.
| 2. What is the Total Probability Theorem? | |
Ans. The Total Probability Theorem is a fundamental concept in probability theory. It is used to find the probability of an event "A" by considering the probabilities of its occurrence under different mutually exclusive and exhaustive conditions. The theorem states that if we have a partition of the sample space into events B1, B2, ..., Bn, then the probability of event A can be calculated as the sum of the probabilities of A given each of the partition events multiplied by the probability of each partition event.
| 3. How is the Total Probability Theorem applied in real-life scenarios? | |
Ans. The Total Probability Theorem is commonly used in real-life scenarios to calculate probabilities in situations with multiple possible outcomes. For example, it can be used in insurance risk assessment to calculate the probability of an accident given different driving conditions (rainy, snowy, clear). It can also be applied in market research to determine the probability of a customer purchasing a product based on different marketing strategies employed.
| 4. Can you provide an example of the Total Probability Theorem in action? | |
Ans. Sure! Let's say there are two factories, A and B, producing a certain product. Factory A produces 60% of the total output, while Factory B produces the remaining 40%. The defective rate of the product from Factory A is 5%, while the defective rate from Factory B is 10%. What is the probability of randomly selecting a defective product? To solve this, we can apply the Total Probability Theorem. Let A be the event of selecting a defective product, B1 be the event of selecting from Factory A, and B2 be the event of selecting from Factory B. The probability of selecting a defective product can be calculated as: P(A) = P(A|B1) * P(B1) + P(A|B2) * P(B2) = 0.05 * 0.6 + 0.10 * 0.4 = 0.03 + 0.04 = 0.07 Therefore, the probability of randomly selecting a defective product is 0.07 or 7%.
| 5. How does partitioning the sample space help in probability calculations? | |
Ans. Partitioning the sample space helps in probability calculations by breaking down a complex event into mutually exclusive and exhaustive events. It allows us to consider different scenarios or conditions under which an event can occur and calculate their individual probabilities. By summing up these probabilities, we can find the overall probability of the desired event. Partitioning simplifies the calculation process and provides a systematic approach to probability analysis.
Text Transcript from Video
hello friends this video on plurality
part 17 is brought to you by exam fear
calm normal fear from exam before
watching this video please make sure
that you have lost power 20 part 60 I
will take a new topic called partition
of a sample space so the set of events T
1 e 2 e 3 tilly n is said to represent
partition of the sample space if if you
take the intersection of any to walk the
set to get Phi that is there is no
common element no common element in
cells
right you take any to said there will
not be any car also if take the
intersect you near of these tools events
you take all the events what you get is
in sample space also provided II of each
of these are non zero that is they have
some formalities that is if you see that
even e1 to en represents a partition of
sample space if they are pairwise
disjoint that is you take any two pairs
they are disjoint right there is no
common element in them their exhaustive
that means if you take all even the
sample space and they have nonzero
values values of each of these is zero I
will Pete once again they have pairwise
disjoint because you take any do pair
doesn't have any common element the
exhaust tip if you take all the elements
you take the union of these you get the
sample space and they have all longitude
abilities now let us take theorem of
total probability so you have already
partitioned my sample space into these
segments you re to en and suppose that
each of this event has nonzero probable
days I have this big sample space and I
had Institue ET v 1e e 2 e 3 en
therefore so many segments I divide this
and let a be any event a be any event
and I want to find the probability of a
then the probability of a has to be
probability of even the first set into
probability of a given even class
probability of second set e 2 interval
value of a given a to you keep doing
this till the NF even you have into
proven T of a given E that is what the
theorem of total probability is it helps
us to find solutions amount of questions
where this particular let's suppose I
have to find the provides a observe even
a where this event is depend on lot of
factors like so what I do is I divide my
whole sample space into law
example let's suppose is property that
the work is done on time right work done
on time and they give me so many events
for example the strike happened the
strike happened right or the labors are
ill or you know what in this III can be
machine is faulty right washing machine
is faulty or there's a holiday holiday
today or it can be there is no power cut
power supply so see for a world to
happen work depends on a lot of factors
sample strike can happen strike happen
the world is humble right if the workers
are only somehow personally the ill thus
the production is hampered the machines
are not working the production happen
the power supplies not the production
happens so the production of a goal
depends on all factors the real world
right so what we do is we drag the whole
thing into the different events and all
these events are mutually exclusive we
see right they are exclusive events and
then we use this formula that the
probably the work done is on time will
be what is the probability that you know
the strike happens and then the strike
happens what is the propriety of the
work is online
what is the prevent is the workers ill
and the work curl is ill what is the
prevalence in the book is done on time
what is the probability that the machine
is faulty right and the machine is 40
there will be some production maybe 20%
30% or the regular rate so what is it
what is the probability or what is the
rate of work done when the machine is
faulty
there is no power supply still some work
can be done right but it'll not be
hundred persons in that case what is it
probably is the water the power supply
went off and when the power supply went
up what was the rate of work done
similarly in the holiday or some workers
come actually so those things taken care
of
so you you end up in this formula saying
that you have one sample space which
depends on a lot of factors you can say
that again divided into these events and
those fast this has to be mutually
exclusive and exhaustive event why
because if you take any two events there
should not be any common elements and
you Club all the event that becomes
sample speed so you convert those who do
events and then you apply the theorem of
duality to get the probability of one
particular task I'll take my example but
similar example is a person has
undergone a construction job the
probabilities are 0.65 that there will
be a strike right point a that a
construction job will become completed
on trying if there is no strike and
point through the construction job will
become little thing there is a strike so
this what I have done is I divided two
events one guy is strike and no strike
only two scenarios they have taken in
this case just to give you a simple
question so they had two events right
strike and go strike so no parity that
is a strike is 0.65 so probability of
there is no strike will be void 3/5
correct not all right here now in this I
have to find the work done this is my
work done this by Volta actually right
let it let this be work done so
probability that the work is done if
there is a no strike if there is no
strike that is if there is no strike the
probability the work that is point eight
zero correct
so while the construction job will be
coming on time if there is strike is
0.32 there is probability of work done
on time if there is if there is a strike
if there is a strike is 0.32 correct for
well default strike is 0.65 right given
these three things are given 0.65 is the
ability of the strike point three five
the morality of those trying and then we
have with some you have some work done
work done is depending on the strike
Ashley so work done if there is no
strike the probability of getting it on
time is 0.8 walk done getting on time
where is a strike is 0.3 t find the
probability that the go up that is on
time so probability that the work done
is on time is nothing bad
so Verity of strike into plural T or
work done all strike class stability of
no strike into poverty or work done if
there is no strife I hope you understand
this the same formula we have used
because we have converted this guy into
only two events strike and now strike so
I am just using this form correct so
true Verity of strike is what 0.65 so
Verity of work done infinitive strike is
0.32
thank you plus so malady of no strike is
what 1 minus point 6 5 that is 0.35
correct point we find in to prepare into
your work done when there is no strike
is pointing all right if you saw this
becomes 0.2 0 I lost this become point
to e 0 and this becomes point 480 and
that is - there is ample so the thing
you have to understand is in
case my work done is depending on
various factors the factors in this
example was tried and non strike so
violently the work does is on time if
the strike is different if there is no
strike is different right the battle is
a different and I have to find the
prevailing the work is done on time
now since work done is depending on
strike an on strike so I what I did was
I divided my holes under squeeze the two
events trying and now strike strike was
65 percent and non strike is 35 percent
right and I have all these probabilities
of the work done it is strike or non
strike then I use my formula to get the
answer this is the application of
theorem of Newton well thank you visit
exam viacom to watch free education
videos try free online tests get the
best quality study materials study from
the best tutors and mentors and much
more thanks and screen
part 17 is brought to you by exam fear
calm normal fear from exam before
watching this video please make sure
that you have lost power 20 part 60 I
will take a new topic called partition
of a sample space so the set of events T
1 e 2 e 3 tilly n is said to represent
partition of the sample space if if you
take the intersection of any to walk the
set to get Phi that is there is no
common element no common element in
cells
right you take any to said there will
not be any car also if take the
intersect you near of these tools events
you take all the events what you get is
in sample space also provided II of each
of these are non zero that is they have
some formalities that is if you see that
even e1 to en represents a partition of
sample space if they are pairwise
disjoint that is you take any two pairs
they are disjoint right there is no
common element in them their exhaustive
that means if you take all even the
sample space and they have nonzero
values values of each of these is zero I
will Pete once again they have pairwise
disjoint because you take any do pair
doesn't have any common element the
exhaust tip if you take all the elements
you take the union of these you get the
sample space and they have all longitude
abilities now let us take theorem of
total probability so you have already
partitioned my sample space into these
segments you re to en and suppose that
each of this event has nonzero probable
days I have this big sample space and I
had Institue ET v 1e e 2 e 3 en
therefore so many segments I divide this
and let a be any event a be any event
and I want to find the probability of a
then the probability of a has to be
probability of even the first set into
probability of a given even class
probability of second set e 2 interval
value of a given a to you keep doing
this till the NF even you have into
proven T of a given E that is what the
theorem of total probability is it helps
us to find solutions amount of questions
where this particular let's suppose I
have to find the provides a observe even
a where this event is depend on lot of
factors like so what I do is I divide my
whole sample space into law
example let's suppose is property that
the work is done on time right work done
on time and they give me so many events
for example the strike happened the
strike happened right or the labors are
ill or you know what in this III can be
machine is faulty right washing machine
is faulty or there's a holiday holiday
today or it can be there is no power cut
power supply so see for a world to
happen work depends on a lot of factors
sample strike can happen strike happen
the world is humble right if the workers
are only somehow personally the ill thus
the production is hampered the machines
are not working the production happen
the power supplies not the production
happens so the production of a goal
depends on all factors the real world
right so what we do is we drag the whole
thing into the different events and all
these events are mutually exclusive we
see right they are exclusive events and
then we use this formula that the
probably the work done is on time will
be what is the probability that you know
the strike happens and then the strike
happens what is the propriety of the
work is online
what is the prevent is the workers ill
and the work curl is ill what is the
prevalence in the book is done on time
what is the probability that the machine
is faulty right and the machine is 40
there will be some production maybe 20%
30% or the regular rate so what is it
what is the probability or what is the
rate of work done when the machine is
faulty
there is no power supply still some work
can be done right but it'll not be
hundred persons in that case what is it
probably is the water the power supply
went off and when the power supply went
up what was the rate of work done
similarly in the holiday or some workers
come actually so those things taken care
of
so you you end up in this formula saying
that you have one sample space which
depends on a lot of factors you can say
that again divided into these events and
those fast this has to be mutually
exclusive and exhaustive event why
because if you take any two events there
should not be any common elements and
you Club all the event that becomes
sample speed so you convert those who do
events and then you apply the theorem of
duality to get the probability of one
particular task I'll take my example but
similar example is a person has
undergone a construction job the
probabilities are 0.65 that there will
be a strike right point a that a
construction job will become completed
on trying if there is no strike and
point through the construction job will
become little thing there is a strike so
this what I have done is I divided two
events one guy is strike and no strike
only two scenarios they have taken in
this case just to give you a simple
question so they had two events right
strike and go strike so no parity that
is a strike is 0.65 so probability of
there is no strike will be void 3/5
correct not all right here now in this I
have to find the work done this is my
work done this by Volta actually right
let it let this be work done so
probability that the work is done if
there is a no strike if there is no
strike that is if there is no strike the
probability the work that is point eight
zero correct
so while the construction job will be
coming on time if there is strike is
0.32 there is probability of work done
on time if there is if there is a strike
if there is a strike is 0.32 correct for
well default strike is 0.65 right given
these three things are given 0.65 is the
ability of the strike point three five
the morality of those trying and then we
have with some you have some work done
work done is depending on the strike
Ashley so work done if there is no
strike the probability of getting it on
time is 0.8 walk done getting on time
where is a strike is 0.3 t find the
probability that the go up that is on
time so probability that the work done
is on time is nothing bad
so Verity of strike into plural T or
work done all strike class stability of
no strike into poverty or work done if
there is no strife I hope you understand
this the same formula we have used
because we have converted this guy into
only two events strike and now strike so
I am just using this form correct so
true Verity of strike is what 0.65 so
Verity of work done infinitive strike is
0.32
thank you plus so malady of no strike is
what 1 minus point 6 5 that is 0.35
correct point we find in to prepare into
your work done when there is no strike
is pointing all right if you saw this
becomes 0.2 0 I lost this become point
to e 0 and this becomes point 480 and
that is - there is ample so the thing
you have to understand is in
case my work done is depending on
various factors the factors in this
example was tried and non strike so
violently the work does is on time if
the strike is different if there is no
strike is different right the battle is
a different and I have to find the
prevailing the work is done on time
now since work done is depending on
strike an on strike so I what I did was
I divided my holes under squeeze the two
events trying and now strike strike was
65 percent and non strike is 35 percent
right and I have all these probabilities
of the work done it is strike or non
strike then I use my formula to get the
answer this is the application of
theorem of Newton well thank you visit
exam viacom to watch free education
videos try free online tests get the
best quality study materials study from
the best tutors and mentors and much
more thanks and screen
About this Video
4.9/5 Rating
Apr 20, 2026 Last updated
Related Exams
Partition Sample Space, Total Probability Theorem (Part - 17) - Probability, Maths, Class 12 for Class 122026 is part of Class 12 preparation. The notes and questions for Partition Sample Space, Total Probability Theorem (Part - 17) - Probability, Maths, Class 12 have been prepared according to the Class 12 exam syllabus. Information about Partition Sample Space, Total Probability Theorem (Part - 17) - Probability, Maths, Class 12 covers all important topics for Class 122026 Exam. Find important definitions, questions, notes, meanings, examples, exercises and tests below for Partition Sample Space, Total Probability Theorem (Part - 17) - Probability, Maths, Class 12.
Introduction of Partition Sample Space, Total Probability Theorem (Part - 17) - Probability, Maths, Class 12 in English is available as part of our Class 12 preparation & Partition Sample Space, Total Probability Theorem (Part - 17) - Probability, Maths, Class 12 in Hindi for Class 12 courses. Download more important topics, notes, lectures and mock test series for Class 12 Exam by signing up for free.
Description
Partition Sample Space, Total Probability Theorem (Part of covers all the important topics, helping you prepare for the Class 12 exam on EduRev. Start for free!
Information about Partition Sample Space, Total Probability Theorem (Part - 17) - Probability, Maths, Class 12
Here you can find the Partition Sample Space, Total Probability Theorem (Part - 17) - Probability, Maths, Class 12 defined & explained in the simplest way possible. Besides explaining types of Partition Sample Space, Total Probability Theorem (Part - 17) - Probability, Maths, Class 12 theory, EduRev gives you an ample number of questions to practice Partition Sample Space, Total Probability Theorem (Part - 17) - Probability, Maths, Class 12 tests, examples and also practice Class 12 tests.
Related Searches
Extra Questions, Exam, Summary, Viva Questions, ppt, Total Probability Theorem (Part - 17) - Probability, mock tests for examination, Semester Notes, Total Probability Theorem (Part - 17) - Probability, past year papers, Total Probability Theorem (Part - 17) - Probability, Class 12, Partition Sample Space, Objective type Questions, Partition Sample Space, Free, Maths, Class 12, Sample Paper, shortcuts and tricks, video lectures, Maths, Class 12, Maths, Important questions, pdf , MCQs, Previous Year Questions with Solutions, Partition Sample Space, practice quizzes, study material;