What are Bernoulli Trials? - Probability, Class 12, Math Video Lecture | Mathematics (Maths) Class 12 - JEE

now let us know what are Bernoulli
trials but nolle trials are related to
what we started in the previous video
that means they are related to
dichotomous alternatives now dichotomous
alternatives are the ones as we said in
the previous video which result in a
success or a failure
that means if I say the tossing of a
coin if I say the manufacturing of a
product the coin that is tossed may
either result in a head or a tail so
what is favorable suppose head is
favourable to us then tail is considered
as a failure similarly if I say about
the manufacturing of a product it may be
either defective or non defective so
that is also important the other thing
that I want to tell you that in case of
Bernoulli drivers I know that the
definition should have a huge importance
because only then we can understand a
concept better so but knowledge trials
are those which follow each of the
following characteristics the first is
they are finite in number they are
finite in number that means you can
count them very easily the second is
they are independent they are
independent the third is after you have
considered even they are independent the
third is the each trial the each trial
results in either success or failure
that means you can classify you are not
confused whether this has a success or a
failure or ambiguous nature and the last
but not the least is that the
probability of success or failure
remains the same in each trial so
probability of success or failure
remains remains same in each trial
now with these points in mind let me
take an example suppose there's a back
and the bag has say five black balls and
six green balls so five black balls and
six green bio balls are a part of the
back now what we are thinking office we
are finding the probability of taking
out a black ball so that becomes 5 over
11
now again successively if I have to take
out the second black ball and the
question is that it is with replacement
again we will get 5 over 11 in the third
drawl so 5 over along 11 because it is
with replacement but if it is without
replacement so first time it will be 5
over 11 the second time it will change
to some other number then the third
times to some other number because the
number of balls are not being replaced
so the number of balls in totality are
becoming less so that means in the first
case where it was with replacement the
probability of success of failure would
remain the same because the probability
is coming out to be the same but in the
next case that we studied when we saw
that there was different probability in
case of without replacement that case is
of not Bernoulli trials when the first
case of with replacement is related to
Bernoulli trials so now we understand
the basic concept of Bernoulli trials in
the next video we'll be studying about
definition of binomial distribution