About the probability calculator
This probability calculator handles three common situations: combining two independent events, working out odds and repeated trials for a single event, and finding binomial probabilities for the number of successes in a fixed number of trials.
Probabilities are entered as numbers between 0 and 1 (for example 0.25 for 25%) and shown as both decimals and percentages.
Who should use the probability calculator
- Students learning probability.
- People assessing odds in games and simple risk questions.
- Analysts modelling yes/no outcomes repeated many times.
How to use the probability calculator: what each input means
- Mode
- Two independent events, a single event with repeated trials, or the binomial distribution.
- P(A), P(B)
- Probabilities between 0 and 1.
- n, p, k
- For binomial: number of trials, success probability per trial, and target number of successes.
How the probability calculator works: method and formula
For independent events, the chance that both happen is P(A) × P(B), and the chance that at least one happens is P(A) + P(B) − P(A and B). For repeated trials, the probability of at least one success is 1 − (1 − p)^n. The binomial probability of exactly k successes is C(n, k) × p^k × (1 − p)^(n − k), and cumulative probabilities sum the terms.
- Both (independent)
- P(A and B) = P(A) × P(B)
- At least one
- P(A or B) = P(A) + P(B) − P(A)P(B)
- Binomial
- P(X = k) = C(n, k) pᵏ (1 − p)ⁿ⁻ᵏ
How to read your probability calculator result
Events are treated as independent: one does not change the chance of the other. Probabilities must lie between 0 and 1. In binomial mode, the table shows probabilities near k so you can see the shape of the distribution.
Probability Calculator worked example
P(A) = 0.4 and P(B) = 0.3 independent; then 10 fair coin flips.
- Both: 0.4 × 0.3 = 0.12.
- At least one: 0.4 + 0.3 − 0.12 = 0.58.
- Exactly 4 heads in 10 flips: C(10, 4) × 0.5¹⁰ = 210 ÷ 1024 = 0.205078.
P(A and B) = 0.12; P(A or B) = 0.58; P(4 heads in 10) ≈ 0.2051.
Practical uses of the probability calculator
- Checking textbook probability problems.
- Estimating the chance of at least one success in repeated attempts.
- Modelling pass/fail counts in quality testing.
Assumptions and limitations of this calculator
- Assumes independence between events and between trials.
- Binomial mode is limited to 1,000 trials.
- Probabilities are mathematical models; real-world outcomes may not follow them.