Suppose that we repeat a Bernoulli trial some number of times. The geometric distribution helps us to calculate the probability that we have a given number of failures before one success.

By a Bernoulli trial we mean a trial that has exactly two outcomes, say, success or failure. For example, tossing a coin is a Bernoulli trial since there are exactly two possible outcomes – heads or tails. We might be interested in calculating the probability of getting tails (success) at the 8th attempt after getting heads (failure) repeatedly seven times. Such probabilities can be calculated using the Geometric Distribution.

The probability distribution function can be used to calculate the required probabilities. The probability is given by the formula, P(X=x) = p(1-p)^x Here, p denotes the probability of success, and ‘x’ denotes the number of failures before the first successful attempt.

The required probabilities can be obtained by simply entering these values in the calculator below.

P(X = 7): 0.02471

P(X < 7): 0.91765

P(X ≤ 7): 0.94235

P(X > 7): 0.05765

P(X ≥ 7): 0.08235