Calculate the probability of at least one success or no success after N trials from a per-trial chance entered as percent or decimal.

Independent trials with the same chance of success each time.

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Probability Of Success After N Trials Formula

The following formula is used to calculate the probability of success after N trials.

P(X ≥ 1) = 1 - (1 - p)ⁿ; P(X = 0) = (1 - p)ⁿ

Variables:

  • P(X ≥ 1) is the probability of at least one success after n trials
  • n is the nonnegative whole number of independent trials
  • p is the probability of success on a single trial (decimal)

What is a Probability Of Success After N Trials?

This calculator gives the binomial probability of at least one success, together with the probability of no success, in a fixed number of trials. A “success” is defined as the outcome that we are interested in. This concept is used in binomial experiments where each trial is independent and has only two possible outcomes – success or failure. The probability remains constant throughout all trials.

How to Calculate Probability Of Success After N Trials?

The following steps outline how to calculate the Probability Of Success After N Trials using the given formula:

  1. First, determine the per-trial probability p and the number of trials n.
  2. Next, convert a percentage probability to decimal by dividing by 100.
  3. Then, calculate the chance of failure in one trial, 1 − p.
  4. Next, calculate the probability of no success, (1 − p)^n.
  5. Finally, subtract that probability from 1 to obtain the probability of at least one success.

Example Problem:

Use the following variables as an example problem to test your knowledge:

p = 0.6

n = 5

At least one success: 1 − 0.4^5 = 0.98976 = 98.976%. No success: 0.4^5 = 1.024%.