01 - Introduction to Probability - Class 10 - Maths Video Lecture

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hey everybody we are looking at some
lines by Robert Frost from his poem the
road not taking very describes his
journey in a forest coming to a pause
suddenly when the road by which he was
travelling gets diverged in let's
imagine just like and we were also stuck
in a situation so the first thing that
we naturally seek out is some kind of
sign board or help or direction which
can help us in making the decision
between the two rows so the event that
is happening right now is travelling by
a road which we can denote as capital
letter e and clearly the two roads that
we see in front of us make the outcome
of this event so let's denote Road on
our left as a and to our right as V
let's say we don't have any sign that
can help us in choosing between the two
roads then we normally say that there's
a 50% chance of taking either Road a or
B that would be why we say this 50%
because there is clearly no bias towards
any particular row so what we are
talking about here is the chance of
choosing a road and when we talk about
chance we have to remember we talk about
probability it is the likelihood of
something happening or the chance that
an event will take place or we can say
that this certainty that is involved in
an event when we hear these terms we
should be sure that we are talking about
probability and normally it is denoted
with capital letter P so probability of
an event which we can denote as V of e
can actually be calculated with a
formula so it's a ratio between the
number of favorable outcomes to the
total possible outcomes involved in
Elega total possible outcomes are the
total options available to us
and number of favorable outcomes are out
of these options whatever we are going
to consider so options in consideration
will form the favorable outcomes so the
ratio of the options in consideration
from the total options will give us the
probability of an event and this has
always been known as the classical way
of finding the probability so in case of
two roads the chance of taking Road a is
one in Boone and the chance of taking
road B is one in two as well that is why
we say that these both outcomes are
equally likely outcomes but what about
in case of three roads so let's make
three roads we already had road a and
road B let's say there is a third road C
then the probability will be 1 by 3
because there are three options in front
of us a B and C there is only one way I
can choose either of the three roads
there that's why the probability is 1 by
3 if you further go on adding these
probabilities we'll get 3 by 3 that is
equal to 1 also in the case of two roads
where we had only two options the
probability was 1 by 2 if we add them
then again we get 2 by 2 that is equal
to 1 what do we observe you we observe
that probability is involved in an event
if added together they give us a sum
total of 1 and this rule is called sum
of probabilities rule but why does it
happen this way because if we notice
when there was only one road let's say
till this point there was only one
option ahead of us and that option was
favorable to us so the ratio was 1 by 1
which is equal to 1 now when the road
got diverged into many other road so the
probability also gets distributed so
when we add these distributed
probabilities then naturally we get a
total probability of 1 let's come back
to the same situation and this time the
signboard indicates me to go to my left
that is I should take Road a so the
probability now changes probability
becomes 100% because I am 100
of taking it so this event where we are
100% sure is called and sure event and
the probability of such an event is
equal to one so this is the highest
limit where a probability can go it
cannot cross 100% or a probability of
one having said that if there is a sure
event can we say that there is an
impossible event also where let's say
the chance of anything happening is 0%
and the probability is zero so this is
going to be a lower limit then such a
will exist if we say that the direction
indicates that we can take either of the
two roads both the roads are good enough
but I can do it by only taking one road
at a time this means I cannot take both
the roads at the same time so that is
what is impossible
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okay so if both the roads are good just
by instinct if I happen to choose Road a
that means I will not travel by road B
in that case traveling by Road we will
become the complementary and
complementary event is denoted with B
bar
how can we find the probability of a
complimentary event we know that there
is a total probability of one so out of
this total probability we can subscribe
the probability of an event currently
happening so probability of choosing
road B which is a complimentary event we
will subtract from one the probability
of traveling by Road a which was 1 by 2
so probability of choosing road B is
also 1 back
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what do we imply from all of this we
imply that there are two extremes of
probability the lower limit is what we
say the probability of zero where there
is a 0% chance of anything happening and
the highest limit is the probability of
one where there is a hundred-percent
surety also probability of an event can
lie between 0 & 1 just like in previous
case it was 1 by 2 in case of two roads
it was 1 by 3 in case of 3 roads which
means either it will be more than 0 or
it will be less than 1 we can show the
same situation in a simple mathematical
expression probability of an event is PE
we know that it is greater than zero or
it is equal to zero and we know that it
is lesser than 1 or equal to 1 so this
is how we can actually indicate
probability of an event in general now
let us make a checklist of whatever been
done in this session
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