Probability Calculator
Combine two independent event probabilities: and, or, neither.
Results update as you type.
About this calculator
This probability calculator takes the chance of two independent events A and B and works out the key combined probabilities: both happening (A and B), at least one happening (A or B), only one of them, and neither happening. It assumes the events are independent, meaning one occurring does not change the chance of the other. Enter each probability as a percentage between 0 and 100.
The rules it applies are the standard ones for independent events: P(A and B) = P(A) × P(B); P(A or B) = P(A) + P(B) − P(A and B); P(neither) = (1 − P(A)) × (1 − P(B)); and "only A" is P(A) − P(A and B). A pie chart splits the sample space into the four mutually exclusive outcomes (both, A only, B only, neither).
Worked example: with P(A) = 50% and P(B) = 30%, both happen with probability 0.5 × 0.3 = 15%, at least one happens with probability 0.5 + 0.3 − 0.15 = 65%, and neither happens with probability 0.5 × 0.7 = 35%. These four outcomes always add up to 100%.
Frequently asked questions
How do I find the probability of two events both happening?
For independent events, multiply their probabilities: P(A and B) = P(A) · P(B). A 50% event and a 30% event both occurring is 0.5 × 0.3 = 0.15, or 15%.
What does independent mean here?
Independent means the outcome of one event has no effect on the other — like two separate coin flips. If the events influence each other (are dependent), these formulas do not apply and you need conditional probabilities.
How is "A or B" calculated?
P(A or B) = P(A) + P(B) − P(A and B). Subtracting the overlap prevents the shared outcome from being counted twice, so the result never exceeds 100%.
How do I find the probability that neither event happens?
Multiply the chances of each event not happening: P(neither) = (1 − P(A)) × (1 − P(B)). For a 50% and a 30% event that is 0.5 × 0.7 = 0.35, or 35%.
What is the difference between "A or B" and "only one of them"?
"A or B" includes the case where both happen, while "only one" excludes it. "Only one" equals P(A or B) minus P(A and B), counting the two exclusive-either outcomes but not the overlap.
What if the two events are not independent?
These formulas assume independence. If one event affects the other you need conditional probability, P(A and B) = P(A) × P(B | A), and this calculator will overstate or understate the combined chances.
Can these probabilities add up to more than 100%?
The four mutually exclusive outcomes — both, A only, B only and neither — always sum to exactly 100%. Individual figures like "A or B" can be large, but they never exceed 100% because the overlap is subtracted.
API — use this calculator from code
Call this calculator as a free JSON endpoint — no key required. Send the field values below as query parameters or JSON. Read the full API docs →
Endpoint
GET https://calculator.free/api/v1/probability/curl
curl "https://calculator.free/api/v1/probability/?pa=50&pb=30"JavaScript fetch()
const r = await fetch(
"https://calculator.free/api/v1/probability/?" + new URLSearchParams({
"pa": "50",
"pb": "30"
}));
const data = await r.json();
console.log(data.results);Results are estimates for general guidance only, not financial, medical or tax advice.