Estimate exactly one success from many possibilities. Switch modes, review formulas, and download neat result sheets. Understand outcomes clearly before testing models, games, or forecasts.
| Example | Input | Method | Exactly One Result |
|---|---|---|---|
| Three independent events | 0.20, 0.35, 0.10 | Σ [pᵢ × ∏(1 - pⱼ)] | 0.406000 |
| Five repeated trials | n = 5, p = 0.20 | n × p × (1 - p)^(n - 1) | 0.409600 |
| Four repeated trials | n = 4, p = 0.30 | n × p × (1 - p)^(n - 1) | 0.411600 |
Independent events: P(exactly one) = Σ [pᵢ × ∏(1 - pⱼ), where j ≠ i]. This adds every case where one chosen event happens and all others fail.
Repeated equal-probability trials: P(exactly one) = n × p × (1 - p)^(n - 1). This is the one-success case from the binomial model.
Supporting values: P(zero) = ∏(1 - pᵢ) for independent events, or (1 - p)^n for repeated trials. Then P(two or more) = 1 - P(zero) - P(exactly one).
The probability of exactly one event calculator finds the chance that only one event happens. It works for independent events and repeated trials. This helps with planning, testing, forecasting, and decision analysis. You can study rare outcomes without manual expansion.
Many real problems focus on a single success. You may want exactly one machine alarm, one customer conversion, one correct answer, or one system fault. This outcome is different from at least one event. It is also different from the expected value. A dedicated calculator avoids confusion.
Use the independent mode when each event has its own probability. The calculator checks each possible winner. Then it multiplies that event by the failure of all others. Last, it adds all one-event cases. This is useful for separate risks, separate offers, or unrelated triggers.
Use the repeated-trial mode when every trial shares the same probability. This is the classic binomial probability of one success. The formula is compact and fast. It suits quality checks, repeated guesses, simple experiments, and repeated customer actions.
This page reports the exact one probability, zero-event probability, and two-or-more probability. It also shows the expected number of events. In independent mode, it lists each event contribution. That detail explains which input drives the result most strongly.
Students can verify homework steps. Analysts can compare scenarios. Teachers can show event structure clearly. Teams can save result summaries for reports. Because the layout is simple, the calculator stays readable on large screens and mobile screens. That makes quick review easier.
It means one event happens and every other event does not happen. The calculator excludes zero events and excludes cases where two or more events occur.
Use it when each event has its own separate probability and events do not affect one another. This mode is ideal for unrelated risks, offers, or outcomes.
Use it when every trial has the same success probability. It matches binomial situations such as repeated attempts, inspections, guesses, or identical experiments.
Yes. Choose the percent option, then enter values like 20 or 35. The calculator converts them internally before computing the final probability.
It may shrink when event probabilities are very high or when many events are present. In those cases, two-or-more outcomes become more likely.
Yes. It also reports zero events, at least one event, two-or-more events, and the expected number of occurrences for better interpretation.
The contribution table shows how much each event adds to the final exactly-one probability. It helps identify the strongest driver in the model.
Yes. The calculator includes CSV and PDF download options, so you can keep a quick record of your scenario and outputs.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.