L12 : Multiplication theorem on Probability - Probability, Maths, Class 12 Video Lecture

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I will understand new topic our
multiplication theorem on your work and
this is for two elements en effet civil
here and this is nothing but something
which is derived from the earlier
formula earlier I had this formula right
this I know is nothing but intersection
F by P of e the same thing you put this
side what you get is provided to your
intersection F is variety of V into so
well if you're definitely this is what
you get similarly if you see you know I
have this formula for validity of e
given F is nothing but we're into U of
intersection and viability of F or you
get if you see the verity of e
intersection F in everyone whether it be
of F into temerity on each in F so if
you see this is what you and that the
formula so if you want to find the
intersection of the probability of
intersection of ei if you have a
conditional probability of F given e
condition and you know the probability
of e you can just multiply them and get
the answer or if you know the
probability of e even F and also in the
probability of F it can multiply these
two ending it just right that's the
formula we have you can use this formula
so I have a on that contains 10 red 5
green balls
sold it has template and fighting ball 2
balls are drawn from this on one after
another without replacement so I will
take out one and then I am taking out
one whole walls without replacement what
is the probability that both the balls
drawn balls are right so if you see here
if I have my
I said let's suppose F which means first
is read f is for for spread and it
suppose s is for second read I have to
choose so here I have to find the
probability of F intersection s now you
see finding the probability of F is
simple finding the probability of
getting first read is simple and you
know that the formula we are going to
apply is probability of F intersection s
is nothing but probability of F dot
mobility of this given F this is the con
lie beyond so the probability of getting
first grade is very simple we know how
because they are how many ten rates
total number of balls are fifty so
probability of getting a red is ten by
twenty first twenty of getting second
reading given the first is red is how
much that is something we know how to
find okay so that if you see will be
since it was without replacement first
ball is ready given then we are left
with only mine bread balls right nine
red and five the total number of balls
we are left with 14 balls I am to find
probality of getting a second red that
is nine by why because you took out one
red ball you are left with only fourteen
balls and then you are to take out
the next ball and you want that next
ball has to be read so it has the
probability 9 by foot and that is
nothing but to us and that is miles
where is it but just I applied the
formula to get the probability and
there's nothing but multiplication to r1
cabal will take my example where we'll
have three elements instead of two
elements so here we have only two
elements FNS building examples where we
are more than two variables so for this
formula it is simple so if you want to
multiply these global t's probability of
e intersection F intersection G is
nothing but Rho L D of e into
probability of F given e into
probability of G given here it is like
this probability of e into Rho Valentia
of F given e because you only cover this
then probability of G given F any there
is simple we do once again this guy is
our Roberto ality of e into so value of
F given e because you already covered a
super variety of F given E into
probability of D given en F that's why
it is so early of e interpret e of F
given e into probability of G even here
it's not the complex just understand
this Provera G of e intersection F
intercept in G is nothing bar so value
of e into variety of F given E into
parity of G given both ENS correct very
simple let us take my example on this
same formula three cards are drawn
successively without replacement from a
part of 52 will shuffle car what is the
probability that the first you cause a
key and third car isn't is so we have
this structure here so from this three
if you see the car structure we have of
13 I'm uncertain heart 13 clubs are in
splainin
we have this jkq are calm faces and we
have this numbers like this right
so from this we take out three cards c1
c2 n c3 we remind the variety that the
first two cards are king that is we
refined the Vivendi off first card is
king second card is king and the third
card is is first is king second Athene
and Thursdays so this guy is nothing but
if you see is quality of King into
morality of keen to given the first one
is king 1 into probability of a 3 given
the first two cards are king one entity
where is it will now prevail T of king
one is Hamid the first card and hanging
out in this car I have four kings right
holding zap whole is total card is how
much 50 right so priority of King one
will be four by one card is gone from
this now I am left with three King and
51 cards correct so next is probability
of king - given king one I've already
told lad the first guy was king once a
plurality of king - will be XI by 50y
because this is preventing of King 2
given a 1 into so now I am left with 2
king and 50 cards and how many is I have
I asked lab for ace because I'll enter
sighs now I defined the quality of given
the card is is already told that we have
taken out two cards and both are King
card that means I am how many is left
over left total card is 15 this is my
value you saw you get two by five five
play simple
I hope you understand this probability
of first card in second card in your
third cup third card ace is provided
your first card King into probability of
second card King given first card skiing
into the binary of third card is given
the first card is where do your first
card King is very simple poor I have to
do because there for King and old cars
are pity to my reading of second card
King even the first card is female 3 by
51 because from this IP code 1 Kings
omelet with shrinking and 51 cards but
has 3 barranquilla not defined the
probability of getting an ace given the
first two cards I took worse that means
I am left with 50 cards out of which we
have two King and forays right and other
cards also but eighth only 4 so it
becomes 4 by let us take one more
example of a multiplication to your own
providing 2 cards are drawn at random
without replacement from the back to
playing cards find the probability that
both the cards are drawn that means I
have to find the probability of first
card black second guard correct this guy
is nothing but probability of first con
tomate into probability of second card
line given the first guy
how many black cards 26 black cards
right total got 52 so probability of
black card will be 26 by 3 correct first
kiss
second is I told that one car I took and
that is black so I'm late for 25 black
card and 51 total gun so second also I
want to find the morality of getting a
plan so about 50 51 I have 25 black card
so this quality will be 25 by 51 right
because 25 possible options of reading a
black card order to adduce of t1 cards
so this is mine and you solve this this
is nothing but 25 by once ago
there isn't just the application of my
addiction to improve already providing
of B 1 and P 2 is nothing but the value
of V 1 multiplied by the value of VD
given and there is a change my
deflection you can do it on n number of
things let's say couple example so here
a box orange is infected by examining
three orange randoms without Lisa please
note for all these words without
replacement she or enjoy drinking ball 3
or in the world the box is a pill for
sale otherwise resected find the
probability that the box containing 15
oranges out of each 12 of wood 13 our
bags are approvers so I can walk which
has three bad she bad
I say given good and three bad watch and
it is approved only when I take out
three ball three oranges and all are
good that is you get first good second
good and third so when this condition is
true then early my oranges opposite
this guy is nothing bad so variety of
good 1 into probability of getting
second good given the first is good no
value of getting third good right give
it first - although correct so
probability of getting good as how much
how many oranges 1500 how many goats 2l
so order from if you take any of that 12
are in from 15 you get the probability
of getting good now from this one guy is
gone so I am left with 11 good and 3
back correct because 1 is gone so in
this case the probability of getting
second good is 11 by 40
why because 11 good and free back from
this again one guy is gone some left
with 10 good add 3 man so probability of
getting third good also will be 10
goodbye total number of our angels study
and this if you solid nothing but
portico and that is nice there Isabelle
I have this box from this I will take
out three oranges all three are good I
say that my box is a proof so the
probability of a prove for sale is 44 by
19 if you see the only three bad ones
but almost 50% of them are getting
visited and thus for the quality check
is if you see only three are bad but
still 50% of them are getting rejected
because other quality correct
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