Math & statistics
Geometric Distribution Calculator
For “how many tries until the first success” problems: enter the success probability and get exact geometpdf / geometcdf values with the distribution drawn.
P(X = 3)
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mean μ = 1/p
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SD √(1−p)/p
Frequently asked questions
What is the difference between geometpdf and geometcdf?
geometpdf(p, k) gives P(X = k) — the first success lands exactly on trial k. geometcdf(p, k) gives P(X ≤ k) — the first success comes within the first k trials, which equals 1 − (1−p)ᵏ.
How is geometric different from binomial?
Binomial fixes the number of trials and counts successes; geometric fixes nothing and counts trials until the first success. If the question says “how many attempts until…”, it is geometric.
What is the mean of a geometric distribution?
μ = 1/p. If a free throw succeeds 40% of the time, you expect the first make on attempt 1/0.4 = 2.5 on average. The standard deviation is √(1−p)/p.
What is the probability the first success takes more than k trials?
P(X > k) = (1−p)ᵏ — simply the chance of k straight failures. It is the complement of geometcdf(p, k).
Method: P(X = k) = p(1−p)ᵏ⁻¹ and P(X ≤ k) = 1 − (1−p)ᵏ, where X counts trials up to and including the first success — the TI-84 geometpdf/geometcdf convention.