Probability Calculator Online
Work out the probability of single and combined events — unions, intersections and conditional probability — right in your browser.
The Probability Calculator runs entirely in your browser. The probabilities you enter are computed on your device and are never uploaded to ArrayKit.
Open the Permutation & Combination Calculator
About Probability Calculator
The Probability Calculator finds the probability of single and combined events without you writing out the formulas by hand. Enter P(A) and P(B) in Combined events mode and it returns the complement, intersection, union and "neither" probabilities, toggling between independent events (P(A ∩ B) = P(A) × P(B)) and mutually exclusive events (P(A ∩ B) = 0). Switch to Conditional mode to compute P(A | B) from P(A ∩ B) and P(B), the core building block behind Bayes' theorem. It is built for statistics students checking homework, teachers building worked examples, and anyone estimating the odds of two events happening together, separately, or one given the other. Everything runs locally in your browser — the numbers you enter are never uploaded.
Features
- Combined events mode: enter P(A) and P(B) to get the complement, union, intersection and "neither" probability
- Independent/mutually-exclusive toggle changes how P(A ∩ B) is derived
- Conditional mode computes P(A | B) = P(A ∩ B) / P(B)
- Validates that every probability stays between 0 and 1
- Catches an impossible P(A ∩ B) greater than P(B) before it produces a wrong answer
- Copy the full result set or a single figure with one click
- Instant results as you type — no page reload
- Runs entirely in your browser with no probabilities sent anywhere
How to use the Probability Calculator
- Choose Combined events or Conditional mode
- Enter the known probabilities as decimals between 0 and 1
- For Combined events, toggle whether A and B are independent or mutually exclusive
- Read the union, intersection, complement or conditional result
- Copy the result or the full summary with one click
Example
Input
P(A)=0.5, P(B)=0.5
Output
A∩B 0.25 · A∪B 0.75
Independent events: P(A ∩ B) = 0.5 × 0.5 = 0.25, so P(A ∪ B) = 0.5 + 0.5 − 0.25 = 0.75.
Common errors & troubleshooting
- Probability Calculator shows an error for a value like 75. — Enter probabilities as decimals between 0 and 1, not percentages — use 0.75 for 75%, not 75.
- Intersection looks too high after switching to mutually exclusive. — Mutually exclusive events cannot both happen, so P(A ∩ B) is forced to 0 in that mode. Switch back to independent if the events can overlap.
- Conditional mode shows 'P(A ∩ B) cannot be greater than P(B)'. — P(A ∩ B) is always a subset of P(B), so it can never exceed P(B). Double-check which figure is the intersection and which is the condition.
- P(A | B) is undefined. — Conditional probability divides by P(B), so P(B) must be greater than 0. You cannot condition on an event that never happens.
Frequently asked questions
- What does the Probability Calculator compute?
- In Combined events mode it returns P(not A), P(A ∩ B), P(A ∪ B) and P(neither) for two events A and B. In Conditional mode it returns P(A | B) = P(A ∩ B) / P(B).
- How does the Probability Calculator handle independent versus mutually exclusive events?
- Toggle 'A and B are independent' on to use P(A ∩ B) = P(A) × P(B), or off to treat A and B as mutually exclusive, where P(A ∩ B) = 0 and P(A ∪ B) = P(A) + P(B).
- What is conditional probability in this calculator?
- Conditional mode computes P(A | B), the probability of A given that B has already happened, using P(A | B) = P(A ∩ B) / P(B).
- Why must probabilities be between 0 and 1?
- A probability represents a share of certainty and can never be negative or exceed 1 (100%). The Probability Calculator rejects any value outside that range.
- Does the Probability Calculator upload the numbers I enter?
- No. All the math runs locally in your browser. The probabilities you type never leave your device and are not sent to ArrayKit's servers.
- Can I use the Probability Calculator for dependent events that are not mutually exclusive?
- Combined events mode assumes independence or mutual exclusivity. For a general dependent intersection, use Conditional mode with a known P(A ∩ B) and P(B) instead.
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