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 repeated trials. What is the probability of tossing exactly 5 heads in 10 coin tosses? M successes in N trials is yet another definition for this type of probability problems. The formula relies on factorials (!) and combinations C.

                           N!
  BDF = ------------------ * pM * (1 — p)N — M
                  (N — M)! * M!

or, using a simpler equation of combinations C(N, M):

BDF = C(N, M) * pM * (1 — p)N — M

BDF = the binomial distribution probability;
p = the individual probability of the phenomenon (e.g. p = 0.5 to get tails in coin tossing);
M = the exact number of successes (e.g. exactly 5 tails in 10 coin tosses);
N = the number of trials (e.g. exactly 5 tails in 10 coin tosses = number of trials).