Bionominal appropriation is a discrete likelihood conveyance. This distribution was discovered by a Swiss Mathematician James Bernoulli. It is used in such situation where an experiment results in two possibilities – success and failure. Binomial distribution is a discrete probability distribution which expresses the probability of one set of two alternatives-successes (p) and failure (q). Binomial distribution is defined and given by the following probability function:

Formula

P(X−x)=nCxQn−x.pxP(X−x)=nCxQn−x.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. Discover 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(X−x)=nCxQn−x.px,P(at least 6 heads)=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