Free Geometric Distribution Calculator
Calculate the probability that the first success occurs on the k-th trial in a sequence of independent Bernoulli trials.
P(X = k)
0.08192000
P(X = k) vs Success Probability (p)
How to Calculate Geometric Distribution Probability
Formula
P(X = k) = (1-p)^(k-1) * p
The geometric distribution models the number of trials needed to get the first success. Each trial is independent with success probability p. The probability of needing exactly k trials means k-1 failures followed by 1 success. The expected number of trials is 1/p.
Example Calculation
A basketball player has a 20% free-throw rate. What is the probability the first basket is made on the 5th attempt?
- 01P(X=5) = (1-0.2)^(5-1) * 0.2
- 02= 0.8^4 * 0.2
- 03= 0.4096 * 0.2
- 04= 0.08192
- 05Expected trials until first success = 1/0.2 = 5
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