A walkthrough, end to end.
- 1
Enter the probability of two events A and B (each between 0 and 1).
- 2
Optionally toggle whether the events are independent.
- 3
The calculator returns P(A AND B), P(A OR B), and various complements.
Probability rules
Independent: P(A∩B) = P(A) · P(B). General: P(A∪B) = P(A) + P(B) − P(A∩B). Complement: P(A') = 1 − P(A). Conditional: P(A|B) = P(A∩B) / P(B).
What you can do with this.
Coin and dice combined
P(coin=heads AND die=6) = 0.5 × (1/6) = 0.0833. The calculator handles independent events directly.
P(at least one) shortcut
P(at least one of A or B) = 1 − P(neither). Often easier than computing the union directly. The calculator gives both forms.
Lottery odds
P(winning lottery) extremely small. Use the calculator with independent events when computing chained probabilities (e.g., winning two consecutive draws).
Insurance / risk math
Independent risks compound: P(no accidents) = ∏(1 − P(accident_i)). Use the calculator iteratively for compound risk.
Quality / defect rates
Two independent defect probabilities — what's the probability a part has neither defect? P = (1 − p₁)(1 − p₂). Calculator handles this via complement.
Bayes' theorem (conditional)
P(A|B) = P(B|A) × P(A) / P(B). Foundational for medical-test interpretation, fraud detection, etc. The calculator handles direct conditional from joint probabilities.
Complement (P(not A))
P(A') = 1 − P(A). Useful when 'not A' is easier to count than A. The calculator shows complement automatically.
Probability calculator 2026 — what's current
Foundational stats — unchanged. AI tools handle reliably. Standalone calculator wins for speed and verification.
Frequently asked.
Enter P(A∩B) directly if you know it. The calculator's independent assumption is just one mode. Real-world events are often dependent (e.g., correlated stock returns).
AND: both events occur. OR: at least one occurs (could be either or both). For independent events, AND multiplies, OR uses inclusion-exclusion.
Probability is between 0 and 1. Odds are P/(1−P) — e.g., P=0.75 gives odds 3:1. Used in betting and gambling. Different metric, same underlying math.
No. Calculations run entirely in your browser.