Combine event probabilities and solve binomial problems.
P(A or B) = P(A) + P(B) − P(A and B). With P(A) = 0.3 and P(B) = 0.5 (independent) it is 0.65.
Probability measures how likely something is, from 0 (impossible) to 1 (certain). The first tool combines two events: enter P(A) and P(B), and optionally P(A and B), and get the probability of both, either, neither, only one, the conditional probabilities and a test for independence. The second finds the binomial probability of exactly, at most or at least k successes in n trials.
For counting outcomes see the Permutation and Combination Calculator; for normal-distribution probabilities the Z-Score Calculator; for significance testing the P-Value Calculator. Random simulations: Random Number Generator.
The calculator applies the standard method step by step.
| Item | Value |
|---|---|
| P(A and B) — both happen (independent) | 0.15 |
| P(A or B) — at least one | 0.65 |
| P(neither) | 0.35 |
| P(A only) | 0.15 |
| P(B only) | 0.35 |
| P(exactly one) | 0.5 |
| P(not A) | 0.7 |
| P(not B) | 0.5 |
| P(A | B) — A given B | 0.3 |
| P(B | A) — B given A | 0.5 |
| Independent? | Yes — P(A and B) = P(A) × P(B) |
| Case | P(A or B) |
|---|---|
| P(A)=.3, P(B)=.5 | 0.65 |
| P(A)=.5, P(B)=.5 | 0.75 |
| P(A)=.2, P(B)=.1 | 0.28 |
| P(A)=.7, P(B)=.6 | 0.88 |
| P(A)=.9, P(B)=.9 | 0.99 |
For independent events multiply: P(A and B) = P(A) × P(B). For 'A or B' add and subtract the overlap.
Events where one happening does not change the chance of the other, like two separate coin flips.
The chance of A given that B has happened: P(A | B) = P(A and B) ÷ P(B).
The chance of exactly k successes in n independent trials, each with the same success probability p.
1 minus the chance of none: 1 − (1 − p)ⁿ. Five tries at 20% each give 1 − 0.8⁵ = 67.2%.
No. Probabilities run from 0 to 1 (0% to 100%).
It uses the standard method: P(A ∪ B) = P(A) + P(B) − P(A ∩ B) binomial P(X = k) = C(n,k) pᵏ (1−p)ⁿ⁻ᵏ The full working and a worked example are shown on this page.
Decimal results use standard double-precision arithmetic (about 15–16 significant digits). Tools that work with whole numbers — big numbers, factors, bases, combinations — use exact integer arithmetic, so no digits are lost.
Yes for checking your work and learning the method. The steps and formula are shown so you can understand the answer, but follow your teacher's rules about calculators in exams.
No. Everything is calculated in your browser and nothing you enter is uploaded or saved.
