Statistics Binomial Distribution - Statistics

What is Binomial Distribution?

Bionominal appropriation is also known as a discrete probability conveyance. This distribution probability was introduced by Swiss Mathematician James Bernoulli. It occurs in certain situations where an experiment results in two possibilities - success and failure. Binomial distribution is also called as a discrete probability distribution used to provide the probability of one set of two alternatives-successes (p) and failure (q). Binomial distribution is explained by the following probability function:

Formula

for

P(Xx)=nCxQnx.px
Where −
  • pp = Probability of success.
  • qq = Probability of failure = 1−p1−p.
  • nn = Number of trials.
  • P(X−x)P(X−x) = Probability of x successes in n trials.

Example

Problem Statement:

Eight coins are tossed at the same time. Let’s siscover the likelihood of getting no less than 6 heads.

Solution:

Let pp=probability of getting a head. qq=probability of getting a tail.
Here,p=12,q=12,n=8,P(Xx)=nCxQnx.px,P(atleast6heads)=P(6H)+P(7H)+P(8H),8C6(12)2(12)6+8C7(12)1(12)7+8C8(12)8,=28×1256+8×1256+1×1256,=37256
sol

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