Binomial distribution Introduction Definition Success ans failure Formula Example Nc

1. SUBMITTED BY
ANCHU J S
72O822208009
MBA
BINOMIAL
DISTRIBUTION

2. INTRODUCTION
 The binomial distribution is also known as
Bernoulli distribution.
 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
or failure

3. DEFINITION
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

4. FORMULA
P(x) = nCx px (q)n-x
WHERE,
P = Binomial probability
X = number of times for a specific outcome within
n trails
nCx = number of combinations
p = probability of success on a single trial
q = probability of failure on a single trial
n = number of trials

5. 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
possible outcomes
“success” and “failure”.

6. for example,
 In throwing a die, “we can say getting
six” and “not getting six” are two events.
One is success and other is failure

7. SITUATIONSWHEREBINOMIALDISTRIBUTIONCAN BEAPPLIED
Random experiment has only two
events(success and failure)
Trails are independent
The experiment is repeated the finite number
of times.
Probability for a success in a single trial
remains constant from trial to trial of the
experiment.

8. Propertiesofbinomialdistribution
 Binomial distribution is discrete probability
distribution
 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’.

9. examples
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?
Solution:
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
= 459/512.
Therefore, the probability that the person will attain the target atleast thrice is
459/512.