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Formula

Algebraically speaking -

P(ΣY = r)   =     n! Pr Q(n-r)     for r = 0, 1, 2 ... n
r! (n-r)!
where:
  • P(ΣY = r) is the probability of obtaining a given number (r) of successes in a series of independent trials or in a random sample,
  • r is the number of successes in a sample (= ΣY),
  • (n-r) is the number of failures in a sample (= 1 - ΣY),
  • n is the number of observations,
  • P is the proportion of successes in the population,
  • Q is the proportion of failures in the population