BINOMIAL DISTRIBUTION

BINOMIAL DISTRIBUTION

A binomial experiment is a probability experiment that satisfies the following requirements.

1. Each trial can have two outcomes or outcomes that can be reduced to two outcomes. These outcomes can be considered as either success or failure.

2. There must be a fixed number of trials.

3. The outcomes of each trial must be independent of each other.

4. The probability of a success must remain the same for each trial.

The outcomes of binomial experiment and the corresponding probabilities of these outcomes are called binomial distribution.

Notation for the Binomial Distribution

P(S)     The symbol for the probability of success.

P(F)     The symbol for the probability of failure.

p        The numerical probability of success.

q        The numerical probability of failure.

P(S)=p   and   P(F)= 1-p-q

n        The number of trials.

x        The number of success.

Note that 0 <x<n.

Binomial Probability Formula

P(X) = n!    .p^x...q^n-x

                        ^(n-X)!X!

^{J. Santillan}