Geometric Distribution Calculator
How many trials until the first success? Probabilities, mean, and the memoryless property.
X = trial number of the first success (k starts at 1). Example: p = 0.25, P(first success on trial 3).
① Answer
② Steps
③ Why it works
For the first success to land on trial k, the first k−1 trials must all fail and then one succeeds: (1−p)k−1p. The geometric distribution is memoryless: having failed 10 times gives no “credit” — P(X > m+n | X > m) = P(X > n), just like a coin has no memory.