The theory of probability

  Introduction
  Foundation
  Calculating
  Presize definition
  Binomial distribution
  Hypergeometric distribution
  Combined events
  Inseparable events
  'Ion Saliu's Paradox'
  Combinatorics
  Markov Chains
  Random Walks
  Contacts

The formula is also known as the probability of exactly M successes of K elements drawn in a pool of S favorable elements from a total of N elements. For example, a lotto 6/49 game. The lottery commission draws exactly 6 winning numbers. The player must play 6 numbers per ticket, but the player has the latitude to select from a preferred pool of numbers (e.g. 12 numbers with good frequency). The question becomes: What is the probability of getting exactly 5 winners out of 6 in my pool of 12 numbers from a total of 49 lotto numbers? The formula of probability of hypergeometric distribution answers a question that sounds very complicated, but mostly because of wording.

The 'hypergeometric distribution probability' formula has certain restrictions. They are nasty, especially for a computer programmer trying to implement probability algorithms. Some cases are logically impossible; e.g. '1 of 6 in 10 from 10'.