IntroStatsCalc

Geometric Probability

Probability the first success happens on trial x, with geometpdf and geometcdf.

Inputs

Probability that X is

Results update as you type.

Results

P(X = 4) = 0.1024

The probability of exactly 4 trials until the first success is 0.1024, or about 10.24%.

Geometric (p = 0.2) probability bars for x = 1 to 36. The highlighted bars are the outcomes exactly 4; together they have probability 0.1024.147101316192225283134x

Results

P(X = 4)0.1024
Mean μ5
Standard deviation σ4.4721

On the TI-84

2nd VARS (DISTR) → F:geometpdf( for “exactly”, or G:geometcdf( for “at most”.

geometpdf(0.2, 4)

Show steps
  1. Formula. P(X = x) = (1 − p)x − 1 p = 0.83(0.2) = 0.1024
  2. Mean and SD. μ = 1/p = 5; σ = √(1 − p) ÷ p = 4.4721.

About this calculator

When to use the geometric distribution

Repeat independent trials with the same probability of success p until the first success. X is the number of the trial on which that first success happens (1, 2, 3, …). For example: how many free throws until the first make?

The mean is 1/p. If p = 0.2, you expect to wait 5 trials on average for the first success.

More probability calculators: Counting (nPr, nCr) · Discrete Distribution · Binomial · Poisson