Ref : Design for Six Sigma Statistics (3.1.4.3)

A Bernoulli Trial is a simple experiement with following characteristic :

- Each Bernoulli trial has only two outcome :
- Yes / No
- Pass / Fail
- In an experiment with multi Bernoulli trials, the probability of each of the outcomes is the same in every trial
- In an experiment with multiple Bernoulli trials, all trials are mutually independent.

Suppose :

- p = probability of selecting a defective part
- n = part are selected from a infinite population

What is the probability of selecting exactly x defective parts ?

This situation has 'n' Bernaoulli trial with a constand probability of selecting a defect 'p'. Since the trials are indenpendent, the joint probabilities are products of individual probabilities.

Each possible sample with 'x' defective parts and (n-x) nondefective parts has a probability of

Therefore, the probability that a 'n' sample size from a population with a constand probability fo defects 'p' with have exactly 'x' defects is

This probability model is known as Binomial Distribution

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