Binomial Probabilities

TL;DR

Binomial probabilities refers to the likelihood of a specific number of success in a fixed number of independent trials, where each trial has two possible outcomes ( success or failure ). Binomial probability calculations are used to determine the probability of a certain number of "successes" occurring in a sequence of independent Bernoulli trials.

Fundamentals

• Bernoulli Trials
  • Independent Events
  • Success/Failure Outcomes
  • Binomial Distribution

Calculation Methods

• Combinatorics Approach
  • Binomial Coefficient
  • Probability Formula
• Recursive Formulas
  • Pascal's Triangle
  • Cumulative Probabilities

Applications

• Quality Control
  • Defect Rate Estimation
  • Sampling Inspection Plans
• Risk Analysis
  • Probability of Failure
  • Probability Modeling
• Biological Sciences
  - Generic Inheritance
  - Clinical Trial Outcomes

Advanced Topics

• Poisson Approximation
  • Rare Event Assumption
  • Poisson Probability Formula
• Negative Binomial Distribution
  • Geometric Distribution
  • Waiting Time Problems