This content introduces fundamental concepts in probability: experiments, outcomes, sample space, and events, using practical examples like rolling a die and tossing a coin to illustrate these definitions.
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Hi guys good day It's me teacher RJ our
topic for today Class is all about
experiments outcomes sample space and
then events so without further Ado let's
do this topic now this is very important
CL especially class if you're dealing
with probability because your next topic
class will be probability so before we
proceed to our next topic we need to
understand more what are experiments
outcomes sample space and then events so
Later on Guys we will have example in
rolling a Die and then we will have
example in tossing a coin and then we
will have another example What if we
Roll a die at the same time with toss a
coin we do it together so do not be wor
just because I will give you plenty of
examples for you to really understand
this one so before we proceed to our
example we need to define first the
following terms so let's start with
experiments now experiments are
activities that produce an outcome but
the results cannot be precisely predicted
so example We have flipping a coin and
then rolling a d now we do have many
examples class for experiments another
example drawing Marbles from a bag
drawing a card from a standard deck
flipping two coins rolling two d many
examples L for the experiment but most
commonly used for experiments We have
flipping a coin and then rolling a d now
outcomes are the possible results of an
experiment once again do not be worried
with this one because we will will be
explaining this one with regards to our
examples and then sample space is the
set of all possible outcomes of an
experiment is often denoted by the
symbol s and then events are one or more
of the outcomes of an experiment an
event is a subset of the sample space So
if you call this word subset it means
part of so therefore an event is a part of
the sample space so let's have an example class for you to really understand one.
d you can have two Okay you
you can have four you can have three you
can have five you can have six or one so
once again class the possible results
are what we call the outcome so
therefore our answer for outcomes we can
have one Okay once again when you Roll
this one you can have one you can have
four you can have two you can have three
four 5 and then six so 1 2 3 4 5 si
These are the possible results and we
call this one outcomes I hope it's clear
for you class with regards to outcomes
when you Roll this Die the possible
results are what we called outcomes so
we have four so four is an outcome
another example five we have five
therefore five is an outcome possible
results are what we called outcomes now
sample space is the set of all possible
outcomes so therefore this one right
here is what we called sample space so
one two 3 4 5 6 is the set of all
possible outcomes we call that one
sample space so to make it short just
simply copy this one so sample Space
denoted by letter s capital s so that
would be s equals you put braces braces
and then 1 2 3 4 5 and then 6 that's it
that's it for our sample space simply
copy the outcomes because sample space
is the set of all possible
outcomes now let's talk about events
class an event is a subset of the sample
space so therefore event is just a part
of the sample space Let's have an
example Because if I will say rolling an
even number so This is our event rolling
an even
number now What are those even numbers
class with regards to the sample space
of course we know that even numbers
these are numbers divisible by two so
therefore our answer we have two we have
four we have six so therefore CL our
answer for event we have event is equal
to the set of even numbers in this given
sample space so therefore our answer for
event that would be 2 4 and then 6 we
call this one 2 4 si event class because
2 46 is just part of the sample space
once again CL 2 46 is just part of the
sample space and we call this one event
So our event rolling an even number
therefore our answer that would be 2 4
and then 6 Let's have another example
What if the event is
rolling rolling an add number What are
those add numbers class could you try
this one rolling an add number What
would be your answer class for the event
of course event is equal to What are
those add numbers class that's correct
add numbers that would be one numbers
that are not divisible by two we have 1
3 and then 5 so therefore our answer for
event we have 1 3 and then five so once
CL our event we can have one or more one
or more another example if I will say
rolling a number three Okay once again
if I will say rolling a number three So
what would be your answer class rolling
a number three of course your answer
buse it's just three because you want
number three so therefore our event is
equal to 3 Simple as that class Okay
Simple as that class with regards to
event I Hope it's clear for you class
with regards to event is a subset of the
sample space it's just a part of the
sample space All right now What if you
try this one class you try this one
class our event is rolling a number
rolling a number greater than
4 Okay rolling a number greater than 4
What would be your answer class Okay you
put your answer in comment section down
below with regards to our example number
one our event rolling a number greater
than four So what would be your answer
CL you put your answer in the comment
section down below so let's proceed now
to our second example tossing a coin so
let's have an example let's tossing a
coin All right so let's work on to our
second example class How about tossing a
coin so our experiment that would be
coin Now When you Toss this coin class
what are the possible results when we
Toss this coin the possible results It
Could Be Tail or It Could Be head right
once again buse there are only two
results when you toss this coin possible
results It Could Be Tail or It Could Be
head so therefore those results class
are what we call the outcomes so the
answer for our outcomes that would be
head and then that would be Tail so once
again this I hope you're not confused CL
with regards to the outcomes outcomes
those are possible results Now When you
Toss this coin the results It Could Be
Tail or It Could Be head so therefore
our outcomes that would be only head and
then Tail now sample space is the set of
all possible outcomes now our outcomes
we have head and tail so we just simply
copy this one so therefore sample Space
denoted by capital s equals brace that
would be head So I will just put h for
head and then t for Tail that's it CL
for our sample space now let's talk
about events once again CL events are
one or more of the outcomes of an
experiment now What if the event CL is getting
getting
heads so the event is getting heads What
would be your answer CL now based on the
given sample space once again CL event
is a subset of the sample space now
based on the given sample space We only
have h and then Tail once again We only
have one head and then one Tail now
getting heads That's only one head so
therefore We just simply copy h so
therefore our event that would be simply
copy h that's it CL that's the answer
class in getting heads because you only
have one h on the sample space now What
if the event is getting tails What will
be your answer class getting tails What
will be your answer class that's correct
that would be event is equal to That's
only t because based on the given sample
space We only have one t and then that
would be tails So that's the thing there
class with regards to event event is a
subset of the sample space event is just
part of the sample space so getting
heads there's only one h so simply copy
h h and then getting tails We only have
one t on the sample space therefore
simply copy t So that's the thing there
CL with regards to event so let's
proceed now to our third example tossing
a coin and then rolling a die we do it
together class so what are the possible
outcomes Let's have example number three
class Now let's proceed to our third
example class then Later on CL We will
have our activity now for our third
example CL we Toss a coin and then we
Roll at die at the same time we do together
together
What are the possible results so once
again our experiment there would be
time now What are the possible results
class when you Toss a coin and then you
Roll a die at the same time So what are
the outcomes possible results so let's
try that one we Toss a coin and then we
Roll a die at the same time so we have
tail and then number six All right so we
Toss a coin we Roll it die at the same
time we we have head and then number
three so let's try it again we Toss a
coin we have tail and then number three
so therefore CL it is possible possible
results when you toss a coin and then you
Roll a die you can have number one and
then head right This is possible we can
have number one and then head now this
is also possible that we can have number
one and then Tail Okay once again CL
This is possible that when you Toss a
coin and then you Roll a die we can have
number one and then head we can also
have number one and then Tail So this is
possible class Now you can also have
number two and then head So this is
possible that you can have number two
and then head and this is also possible
that you can have number two and then
Tail right you can have number two and
then ta so when you Roll this di This is
possible that you can have number two it
luns with number two and then head it
luns with number two and then ta Now you
can Actually calculate us the number of
possible results by just getting the
number of outcomes class when you Toss a
coin if you do it individually class for
a coin the number of possible outcomes
That's only two right Because if you do
it individually class for a coin the
number of possible results when you Toss
a coin That's only two right the number
of outcomes That's only two because when
you Toss a coin the results It Could Be
head and tail that's There's No Other
results class That's only head and tail
so therefore the number of outcomes
That's only two one and then two so for
a coin there would be two outcomes now
for a die class so that we can calculate
L the number of results for a die class
the number of outcomes when you Roll
this die that would be six right because
when you Roll this die the possible
results that could be one that could be
two 3 4 five and then six so therefore
the number of outcomes when you Roll
this die that would be six now if you do
it together CL just simply multiply the
number of outcomes 2 Tim 6 once again CL
2 * 6 the possible results there would
be 12 results so therefore CL the number
of outcomes the would be 12 so let's try
that one let's check if we have 12 possible
possible
outcomes All right so once again CL for
a coin that would be zero number of
outcomes that would be head and tail so
the number of outcomes that would be
zero and then for a die the number of
outcomes there would be six because for
a die there would be 1 2 3 4 5 6 simply
multiply this one 2 Tim 6 that would be
12 so therefore if we Toss a coin and
then we Roll a die at the same time we
simply multiply the number of outcomes 2
Tim 6 the ro be 12 so let's check CL if
we have 12 number of outcomes when we
Toss a coin and then we Roll a die so we
have one h one and then head one and
then Tail so 1 two 3 4 so we can also
have number three and then head we can
also have number three and then Tail
right This is possible class when you
Toss a coin you can have head and then
number three So this is possible number
three and you can also have number three
and then Tail So this is possible and
then you can have number number four and
then head You can also have number four
and then Tail so one two 3 f 5 si 7 8 we
can also have number five and then head
we can also have number five and then
Tail we don't have enough space let me
Just write it again
CL since we don't have enough space so
once again we can have number one and
then head we can also have number one
and then Tail so first result we can
have number one and then head one and
then Tail we can also have number two
and then head two and then Tail we can
also have three and then head we can
also have three and then Tail four and
then head and then four and then
Tail so we can have five
head and then five and then tail and
then last results we can have six and then
then
head and then six and then Tail so let's
countless the number of results so once
again As I told you earlier we have 12
possible outcomes so Let's count the
number of outcomes so 1 2 3 4 5 6 7 8 9
10 11 12 So that's correct simply
multiply the number of outcomes for a
coin and then the number of outcomes for
a d and that would be 12 now for the
sample space class simply copy this one
so once again sample Space denoted by
capital s so simply copy this one We
have one and then h one and then head so
one and then Tail so possible results we
have two and then head We also have two
and then Tail so we have three and then
head once again the sample space is the
set of all possible outcomes so simply
capy is one class so we have three head
number three and then head we can also
have number three and then
tail and then four and then head also
have four and then
Tail five and then head we can also have
five and then
tail and then six head we can also have
si and then
Tail so These are the sample space class
so I Hope it's clear for you class with
regards to sample space now let's about talk
events class event is a subset of
the sample space so let's have an
example CL if the event class getting an even
even
heads Now what would be your answer
class if the event is getting an even
number and then heads so once again CL
event is just a subset of the sample
space So you look at the sample space
class you have an even number and then head
head
so our answer that would be set of all
events getting an even number and then
head So this
one getting an even number so once again
we cannot include number one Because one
is not an even number once again an even
number those are numbers divisible by
two so one is not included How about
this one CL can we include this one two
and then head Yup getting an even number
and then head so therefore we can
include this one so that would be two
and then head so that would be Our first
answer how about this one CL can we
include this one two and then Tail Nope
we cannot include this one two is an
even number but this is Tail once again
our event getting an even number and
then heads Okay you want heads class
even number and then heads so therefore
we cannot include this one two is an
even number but this is Tail So three is
not an even number three is not an even
number How about this one do four and
then heads Yep we can include this one
because four is an even number and then
we have
heads so that would be four and then
heads Okay another example we have four
and then Tail So we cannot include this
one because this is Tail four is an even
number but this is Tail so five noe five
is not an even number How about this one
plus that's correct we can include this
one six is an even number and then we
have head so that will be 6 and then
head that's it guys that's our first
answer so let's have another example CL
for the event So what if I say so event CL
CL
getting getting a number five on a Die
and then Tail on a coin so getting a number
five getting a number
So what would be your answer getting a
number five on a Die and then Tail on a
coin so once again you want five on a
Die and then Tail on a coin so check
plus the sample space Do we have five on
a Die and then Tail on a coin Yup we
have number five on a Die and then Tail
on a coin So this will be our answer
class because an event is just part of
the sample space so therefore this will
be our answer so event So that would be
and then once again getting number five
and then Tail on a coin five and then
Tail that's it CL that would be your
answer class now How about you try this
one class and then you put your answer
in the comment section down below our
last event class getting tail and a
number greater than three so once again
CL getting tail and a number greater
than three So how about you try this one
CL and then you put your answer in the
comment section down below let me check
CL if you really understand our topic So
you check the sample space once again
our event getting tail and a number
greater than three So you check this one
outl with regards to the sample space
All right so let's proceed now class to our
our
activities All right so let's proceed to
our first activity so once again we're
going to determine the experiment
outcome sample space and then event So
two coins are Toss and landed on ahead
and tail respectively so once again CL
our experiment that will be tossing two
coins sim continuously or tossing two
tossing two coins
simultaneously or tossing two coins at
time now when you toss this coin class
the outcome so let's try that one we can
have head and then Tail So toss this coin
we can have head and then head so
therefore possible outcomes we can have
head and then head we can also have head
and then Tail we can also have tail and
then head we can also have tail and then
Tail so we do have four possible
outcomes because if we do it
individually class As I told you earlier
with our third example if we do it
individually for a coin that's two only
outcomes right possible outcomes for a
coin That's only head and then Tail so
therefore CL the number of possible
outcomes for one coin That's only two
because That's only head and tail
and for another coin That's only two
also because That's only head and then
Tail if you multiply this one the number
of outcomes
individually 2 Tim 2 2 Tim 2 that would
be 4 So that's why class you have four
possible outcomes for two coins because
2 Tim 3 that would be f So that's why we
have head head head tail tail head and
then tail tail so 1 two 3
4 All right so for the sample space once
again sample space is the set of all
possible outcomes so simply Cy this one
denoted by capital s so sample space set
of all possible outcomes so we have H H head head head
