ANCHU J S
The binomial distribution is also known as
This theory is propounded by Swiss
Mathematician a ‘James bernouli’ in 1685.
It is a process through which one can arrive
the result of the experiment mainly success
In probability theory and statistics ,the
binomial distribution with parameters n
and p is the discrete probability
distribution of the number of successes
in a sequence of n independent
experiments , each asking a yes –no
question ,and each with its own Boolean –
valued outcome :SUCCESS OR
P(x) = nCx px (q)n-x
P = Binomial probability
X = number of times for a specific outcome within
nCx = number of combinations
p = probability of success on a single trial
q = probability of failure on a single trial
n = number of trials
SUCCESS AND FAILURE
Consider an event associated to a random
experiment . when the random experiment is
repeated a number of times ,the event may or
may not occur in each of those experiments .
the occurance of the event may be named as
“success” and non-occurance , “failure”
Therefore Random experiments has only two
“success” and “failure”.
In throwing a die, “we can say getting
six” and “not getting six” are two events.
One is success and other is failure
Random experiment has only two
events(success and failure)
Trails are independent
The experiment is repeated the finite number
Probability for a success in a single trial
remains constant from trial to trial of the
Binomial distribution is discrete probability
The shape and location of binomial distribution
changes as ’p’ changes for a given ‘n’.
Binomial distribution has mean= np
Standard deviation =√(npq)
Mean of the binomial distribution changes as
‘p’ changes for a given ‘n’.
The probability that a person can achieve a target is 3/4.The count of tries is 5.
What is the probability that he will attain the target at least thrice?
Given that, p = ¾, q = ¼, n = 5.
Using binomial distribution formula, we get
P(X= x) = nCx .px (q)n-x
Thus, the required probability is: P(X = 3) + P(X=4) + P(X=5)
= 5C3 · (¾)3 (¼ )2 + 5C4 · (¾)4 (¼ )1 +5C5 · (¾)5
Therefore, the probability that the person will attain the target atleast thrice is