Class 10 probability Video Lecture

students welcome to new session and in
this session we will learn a new lesson
probability in our day-to-day life we
come across the sentences such as it may
rain today
sometimes we see probably sanjaya built
of the class or sometimes we hear the
sentences when there are the cricket
tournaments that there is a 50/50 chance
of winning a toss
so in this sentences the words like me
probably chance these words denote
uncertainty this shows that in our
day-to-day life we have to sometimes
deal with the uncertainty and therefore
there is a branch in mathematics that is
developed to measure this uncertainty
and that branch is spoiled as the
probability so we define probability as
the science which measures the degree of
uncertainty
it's called probability students now let
us take few examples to make the ideas
more clear about uncertainty and the
measure of this uncertainty known as
probability let there are two walls one
is black ball and the other is a red
ball and I told you to pick up one ball
out of these two walls I know that you
will either pick up black ball or you
will pick up red ball but I do not know
which one you will pick up so the
possible outcomes I know but the result
I do not know
and this is called as the uncertainty
because I do not know the result whether
it will be black or whether it will be
the red then what are the chances of
picking up the black ball and what are
the chances of picking up the rare ball
definitely there are only two walls one
black and one red so both will how the
equal chances that is 50/50 percent and
in the language of probability it will
be half and it will be half so both
balls will have equal that is half half
stances but if I added one more red ball
and I told you now pick up one out of
this three balls then I know that either
you will pick up this black ball or you
will pick up this red ball or you will
pick up this red ball so there are three
possible outcomes that I know but I do
not know whether you will pick up this
first ball or you will pick up this
second ball or you will pick up this
third ball then what is the probability
of picking of this first ball then it
will be what one-third 1 upon 3 and what
is the probability of picking the red
ball since there are two red balls
whether it is picked up the second one
ball or the third one ball then the
probability will be 2/3 now here there
are two red balls and therefore the
probability of picking up the red balls
beats increase and the probability of
picking up the black ball is degrees now
take the another example if we toss two
points simultaneously then the outcomes
will be either both points will how head
or both points will turn up with tail or
one will turn up tail and the other will
turn up with here and the fourth
possibility is that one with head and
the other militant of with taser
so here the possibilities are for that
we know but what will be the result
whether it will be head whether it both
will be tail or one head and other tail
or one tail and other head we do not
know the final result so this is called
as the probability we know the possible
outcomes but we cannot certainly tell
the result and this because we are
uncertain about it and this is called as
the uncertainty now if I ask then what
is the probability of getting both heads
here it is head here they're both heads
know both heads know BOCES so there is
one favorable outcome and total outcome
will be four and so the probability of
getting both heads will be 1 by 4
suppose I asked that what is the
probability of getting at least one here
at least one head here it is head here
it is here and here it is also one here
at least one head who are there but
there is at least one here so these
three are favorable outcomes so the
total outcome is 4 and the favorable is
3 and therefore the possibility of
getting at least one tail that will be 3
by 4 now before going to the topic
probability let us learn the related
terms of the probability so the first
term is experiment when we toss a coin
we either get head or a tail but the
tossing of a coin is an operation and
this operation is called as experiment
when we throw a die or when we roll a
die
this rolling of a die is called as an
experiment suppose there are three carts
I mean a playing card and you have been
told to draw out one third out of the
three cards and you choose to draw one
card and this card
drawing it's called as an experiment so
when you draw a card that action is
called as an experiment therefore we
define experiment as it is an operation
which can produce some very defined
outcome now very defined outcome means
what we know that in these three cards
there is six of Hearts ten of diamonds
and four of heart so we know what will
be the outcomes outcome may be six of
Hearts outcome may be King of Diamonds
or outcome may be four of hearts so
these are the well-defined outcomes and
out of these three outcomes one is going
to produce and therefore we say it is an
operation which can produce some
well-defined outcome now let us see the
another term that is a random experiment
here is a jar and in jar there are some
geometrical figures there are two types
of geometrical figures one is a
rectangular shape and other is
triangular shape and you have in two
to take out one shape out of the charm
so what will be the possibilities it
will be either a rectangular shape or a
triangular shape and so we know the
outcome will be a rectangular shape or
the triangular shape but we cannot say
certainly that it will be only a
triangular shape or only a rectangular
shape if we draw out or take out one
shape we cannot say it will be a
triangular shape or it will be
rectangular shape but out of these two
it's possible but it is possible
suppose we toss a coin it may be held or
it may be think so two possibilities are
there that outcome we know it will be
either here or it will be a tail the
possibilities we know but we cannot
surely say whether it will be a head or
it will be a tail suppose there is a
spinning field if we spin the arrow it
may stop at one it may stop or two it
may stop at three four five or six out
of the six it may stop at any point so
we know the outcome but we cannot
certainly say that the pointer is going
to stop at six only and so the random
experiment is defined as an experiment
in which all the possible results are
known in advance but none of them can be
predicted certainly we cannot predict
the outcome we know the possibilities
but we cannot predict the predict the
certainty and such experiment is called
as random experiment now let us see the
another term that is outcome
outcome is the result of a random
experiment
it's called as an autumn the result of a
random experiment that is called as
autumn if we toss a coin it turns up to
behave so the outcome is head result is
head which means the result of that
experiment is head and so we call it as
a outcome
suppose we again throw a coin and it
turns up to be tail
it means the result is still and so the
outcome is T if we throw a dime or if we
roll a die in this case the result in
six and so we call the result in six
therefore the outcome is six
there are three cards and you have been
told to take out or draw one card out of
it so you draw one card out of it and
that is six of Hearts so the result is
six of Hearts and so the outcome is six
of Hearts and therefore we define the
outcome as the result of a random
experiment and that result is called as
the outcome now the another term is
sample space suppose we toss a coin it
will be either head or a tail so two
possibilities are there if we throw a
die then the possibilities will be
either it will turn up one or two or
three or four or five or six so six
possibilities are there if we
flip two coins they both coins may turn
up with head or both coins may turn up
with tail or one coin may turn up with
tail and another will turn up with head
and in the fourth case the first coin
may turn up to be head and another may
turn out to be tail so there are the
four possibilities and this set of all
the possibilities is called at sample
space and this sample space is denoted
by s and it is shown into a curly braket
head or tail so first we tossed a coin
so after tossing the coin we either get
head or tail that are the two
possibilities so sample space will be
head or tail and the number of sample
space that will be denoted by n of s
which is equal to two because there are
two possibilities in the second case
where the die is thrown then the six
possibilities are there so the sample
space will be written as 1 2 3 4 5 or 6
and the number of sample space will be 6
here now here in the third case the two
points are tossed and so in the first
case both were turned up to be head in
the second case both were turned to be
tail in 1 was still one was head and one
was head and other was tail and so in
this case the sample space will be given
as HH tail tail tail head or a
tea so this will be the sample space and
the number of sample space in this case
will be four so in the first case NS
will be two in the second case number of
sample space will be six and in the
third case the number of sample space
will be four therefore the sample space
is defined as the set of all the
possible outcomes so the set of all
possible outcomes is called as a sample
space let us see the another term that
is favorable outcome when we throw a die
we may get either result as one or two
or three or four or five or six
and if we consider the chances of
getting even number this is the
condition given to us that chances of
getting even number so out of these six
possibilities we will search for the
even number so 2 is the even number 4 is
the even number and 6 is the even number
and so 2 4 & 6 are the favorable numbers
and therefore the favorable outcome will
be 2 4 & 6 therefore the favorable
outcome is defined as the outcome that
satisfies the given condition are all as
the favorable outcomes here the
condition is getting even numbers and
even numbers are 2 4 & 6 and these are
satisfying the given condition and so
this 3 will be called as the
favorable outcome and favorable outcome
is denoted by a and so the it is written
as ay is equal to into curly bracket two
four and six and number of favorable
outcome is denoted by n of a and so here
in this case the number of favorable out
three outcomes will be three so number
of favorable outcome is equal to three
now let us see the another important
thing that is a range of probability
here's the example that a horse will
grow wings and fly it is not possible at
all
it is impossible thing horse cannot grow
wings and therefore horse cannot fly
this is the impossible thing it is not
going to happen it is not going to occur
see the another example getting seven if
die is so if you die if you throw a die
you will never get six because there are
only one to six numbers they see the
third example getting a green color man
there are two colored man's one for our
of blue colors and one is of red color
there is no green color man and so it is
impossible to get a green colored man
and when there is impossibility of
happening anything then the probability
will be of course zero because there
will be no chance of occurrence so in
this case the probability will be zero
see the another examples that getting a
cream here there are four greens in a
hand and if I told you to
take out one card and asked you what are
the chances of getting a twin definitely
all four cards are clean and there were
there is 100% chance and so in such case
the probability will be 1 then getting
an even number there are four cards and
on all four cards there are the even
numbers even if you take out this card
even if you take out this card or this
or this you are surely going to get an
even card so there is a hundred percent
chance of getting a even card and then
the probability will be 1 so when there
is a hundred percent chance of
occurrence the probability will be 1 and
whenever there is a impossible thing to
happen then the probability will be 0
and so we can say that the probability
ranges from 0 to 1 now let us see the
properties of probability of an event
the first property is the probability of
Scheuer event or certain event is always
1 the second thing we have seen that the
probability of impossible event is
always 0 and therefore we can say that
the probability of an event ranges from
0 to 1 so probability of an event is
always greater than 0 or equal to 0 or
it will be less than 1 or equal so the
probability of an event will never be
negative and will never be greater than
1 and so we can say that the probability
of an event plus probability of not
event that will be always equal to 1 so
students here we will stop
and in this session we have seen the
basic things about the probability and
now in the next session we will see the
problems that are related to the
probability thank you very much