L19 : Bayes theorem : Examples-1 - Probability, Maths, Class 12 Video Lecture

hello friends this video on multi-part
19 is brought to you by exam fear calm
no more free from exam before watching
this video please make sure that you
have watched part 1 to part 18 take one
more example on the base theorem so now
question say they have three identical
boxes one two three each with two coins
box one has both gold coins box two has
both silver coins and box three have one
bold ones River a person chooses a box
at random so I'll draw the chart first
you select you can select box one box
two box three all with equal probability
1 by 3 1 by 3 n right this is going to
choose box at random and takes out the
console this anything if you see is some
let's suppose a bigger box are in some
dark room we don't see this it take out
one coin right and this kind is gold
coin right what does the probability
that other coin in the box is also gold
so if the coin is gold other coin
awesome over that I am talking about the
box one hope you understand this it is
told that the coin I took it's gold coin
and finally I want to find the Cavalia
the other coin is also gold
that means I am talking about the box 1
I want to find the quality that the box
selected is box 1 given that the coin is
this is what I have to find hope you
understand it because stole that you
take out one coin and find the probality
to the other coin left in the box is
gold that was I talking about
box number 1 this guy is nothing but if
you flip it this becomes G by V 1 into
interval D of V 1 by this is G Quebec
correct
nah let's see if you select box one
where we have gold is one because you
have both golds
if you select box to provide Liam gold
is zero because there is all silver you
select box three Coverity or selecting
gold is one waiting why I am doing holy
for God because I'm working only wave
also I can do what silver also but among
encrusted I need only pooled so I wrote
in spa so this part now is preventing of
Gold's selected Beaman Beaman is
selected now this is my benchmark the
wealthy of gold nor will be one right
condition provided if ability of world
selecting even I am doing using that
graph thing since demon is selected not
even as a benchmark of any of gold
annoys one and not prevent your b12 when
do select move is 1 by 3 1 by 3 divided
by probability of selecting gold can
select goal using 3 path right one path
is this one path is this and one
particles you select the first path so
either is 1 by 3 into 1 because here we
get 1 Coverity second path is 1 by 3
into 0 plus alpha 3 u 0 third father is
1 by 3 1 by 2 right 1 by 3 into 1 by 2
because there is a hefty possibility
that it will be cold time because they
have two coins so if you solve this you
get 3 by 3 and that is very simple
Verity that you got the gold from box 1
was to buy easy early not difficult this
part is you have to understand that you
request top of this V 1 G becomes G 1 GB
1 into quality of diamond why poverty
action so let us take one more example
now so the question says a laboratory
blood test is 99% effective in detecting
a certain disease when it is there so it
is there my dream us time to do fine
disease however the test also he has a
foster post positive result for 0.5
custom of the
a person tested right
if 0.1% of population actually has
disease what does the providing person
have the disease given their them this
test reserve this posture so let's first
draw the graph so a person can be
healthy
a person can be healthy a person can th
one other person can be patient right
well if there is it is the persons
having disease if the person is having a
disease ninety nine percent time it is
effective that means ninety nine percent
it will give you a correct result right
one person it will give your incorrectly
but if the person is healthy five
percent times
sorry point five percent times it will
give you a incorrect result right and
ninety nine point five percent times it
will give you a correct listen correct
if point one person of the population is
actually having disease so patient is
0.1 percent and this healthy is
ninety-nine point nine percent that
means this is my whole population in
this 99.9 percent healthy people end
point one question people are preaching
right so if on this patient if you take
this test then ninety nine percent you
get correct result only one person can
get incorrect result but I'm healthy
people if you take this test point five
percent times you get incorrect result
and ninety nine point five persuade you
get correct reason right now I have to
find the probability that the person has
a disease so now this guy is providing
the person
and the disease give me that the test is
result is positive right result positive
are positive so in this case let's find
this if this guy is healthy and you are
getting a incorrect result that means I
am talking about positive result that is
watch it
see if guy is healthy and you are giving
incorrect result that means the result
is guys correct guy is healthy but you
are giving an incorrect result you are
saying guys positive guy is healthy
being positive result that means the
result is negative result is positive
means means result says that person has
do this please note this when you say a
result is positive that means result say
that person has disease so 5% point
fighter person I on any person also it
says that it has zero right on page a
and 99% time is correct since the other
patients is where the actual is having a
disease so this guy is positive in this
case please note here in case of healthy
people incorrect result means positive
and in each of placing correct result
means false hope you in the sentence
right so this is the result this is the
trick part in this question here so what
a healthy person if you are getting
positive that means the result is
incorrect for a patient if you are
getting positive that means reserve this
card okay so we have to find probe aren
t that this guy is diseased or that
means you can say there is a patient
given it is positive this guy is nothing
but Coverity of you topple this
the result is positive given it is
patient into preparatory it is a patient
by priority is result is fault correct
rivality result is positive given
patient if this guy is a patient you put
this benchmark so probability result is
positive is 99% that is 9900 into so
piratey it is a patient is 0.1 that is
0.1 by hundred correct / so Verity that
the result is positive we have two
scenarios one this path and one this
part will take both path so we take this
path first so this guy becomes 99.9
percent is 99.9 into 100 this guy in 2.5
percent right you have taking this path
this bar in 2.5 percent is 0.5 500 plus
you take another part for all positive
this guy that is 0.1 percent is 0.1 by
100 into 99 percent 99 right so if you
solve this what you get is all right
here 22 by 1 and that is fast that is
the probability that the patient is that
the person is patient when the result is
post correct so it is not even 1/5 if
you see not even 20 percent so it's
almost 20 percent the result is positive
into any percent chance are that your
patient you may not be vision but is
this true generally gently if you see
this is a very high percent many person
that means if only 20 wasn't the chance
the test is giving correct result who
pass the test but the cash here is jelly
on healthy person we don't go for test
we go for test only unhealthy person and
so that is the catcher so in this
example assume that everybody went
further test le in a really personal if
you see how we got this so we have this
healthy be polite and benign was
impatient point one person on healthy
people you get ninety nine point five
percent chance negativism on but one
point five percent you get positive
result for patient 99 percent time you
get positive result and one person time
you get garlic we'll take one more
example of a factory which manufacture
Bulls machines here the factory which
manufacture has been the world's machine
a B and C manufactures respectively
twenty five thirty and forty percent of
the world's so they are three machines a
BNC life is machine TVNZ this guy is 25
percent
this guy is 38 percent and C is 40
person of the world of their output five
four and two persons are defective this
guy's five percent effective this guy's
whole person and his guys universalistic
detective the board so that his drawl is
not diagram this guy is a factory
pushing me machinery right so this guy
gives 25 percent this guy gives the fine
person and this guy is awesome
out of these five percent heart
defective out of this whole person are
defective and out of these two cards in
dumb nigga this is what the question is
see they are not defective also which
I'm not writing but these are defective
ones right not defective or I think so
so a bolt is drawn at random from the
product and found to be defective find
the probability that it is manifesting
from B that means I defined the
probability that it is
manufactured by be given it is defective
with the same formula applied will
topple this physical ability of
defective given from B into probability
of B by a frivolity or defective so
probability of defective given B is what
you take D as benchmark for value of
defect is 4% for 100 inter propel into
your beef a variety of these 35 percent
because 35 percent boards are strongly
divided by parity of defective so you
get defecting from three paths one path
is this another path is this another
possible this it will take all this path
path is 25 100 into 500 Part B is 3,500
into 400 path C is 40 by hundred by
hundred right this is what you get so we
solve this you get to any by 69 and that
is your hands well is it because you
just understand that base here is very
critical in such kind of situation you
just have this you write the first thing
you should write that you are looking
for ability of the board from the queue
it is defective then you just use a base
here top of this x PR be e by D and yeah
that's 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