Calculator Inputs
Example Data Table
| Scenario | Model | Inputs | Success Probability | Interpretation |
|---|---|---|---|---|
| Quiz pass chance | Direct ratio | 18 favorable, 25 total | 0.72 | Seventy two percent success chance |
| System uptime target | Complement rule | Failure probability 0.08 | 0.92 | Success comes from one minus failure |
| Sales calls | Binomial exact | 10 trials, 6 successes, p = 0.55 | 0.23878 | Exact hit count in repeated trials |
| Quality checks | Binomial at least | 12 trials, at least 9, p = 0.8 | 0.55835 | Meeting or exceeding the target |
| First win timing | Geometric | First success on trial 4, p = 0.3 | 0.1029 | First success occurs after three misses |
Formula Used
Direct ratio: P(success) = favorable outcomes ÷ total outcomes.
Complement rule: P(success) = 1 − P(failure).
Binomial exact: P(X = k) = C(n,k) × pk × (1 − p)n−k.
Binomial at least: P(X ≥ k) = Σ C(n,i) × pi × (1 − p)n−i, for i from k to n.
Geometric first success: P(X = k) = (1 − p)k−1 × p.
For repeated independent trials, the expected number of successes is n × p, and variance is n × p × (1 − p).
How to Use This Calculator
- Select the probability model that matches your scenario.
- Enter the required inputs for that model only.
- Press the calculate button to display the result block.
- Review the probability, percentage, odds, complement, and notes.
- Download the result as CSV or PDF if needed.
- Compare different models to test assumptions and planning targets.
FAQs
1. What does success probability mean?
It is the likelihood that a chosen event happens. The value ranges from 0 to 1, where 0 means impossible and 1 means certain.
2. When should I use direct ratio mode?
Use direct ratio when you already know favorable outcomes and total possible outcomes. It works well for simple counting problems and equally likely cases.
3. Why is the complement rule useful?
It helps when failure is easier to estimate than success. You subtract the failure chance from one to obtain the success probability.
4. What is binomial exact probability?
It measures the chance of getting exactly a chosen number of successes across a fixed number of independent trials with the same success rate.
5. What does at least k successes mean?
It adds the probabilities for k successes, k+1 successes, and every larger count up to the total number of trials.
6. When is geometric mode appropriate?
Use geometric mode when you want the chance that the first success occurs on a specific trial number after earlier failures.
7. What assumptions matter most here?
Repeated-trial models assume independence and a constant success rate on each trial. If those assumptions fail, results may be misleading.
8. Can I export the calculated result?
Yes. After calculation, use the CSV or PDF buttons to save the visible result summary for reporting, documentation, or later review.