How to use the Probability Calculator
- 1. Pick a problemTwo events, binomial, Bayes' theorem, or at least once in n tries.
- 2. Enter probabilitiesType values between 0 and 1; the tool checks they're consistent.
- 3. CalculateSee every related probability with the formula used.
The rules used
For two events: P(A or B) = P(A) + P(B) − P(A and B). If they're independent, P(A and B) = P(A) × P(B); if mutually exclusive, it's 0. Conditional probability is P(A | B) = P(A and B) ÷ P(B). The binomial distribution gives the chance of exactly k successes in n independent trials with chance p each. Bayes' theorem turns a test's accuracy into the chance you actually have a condition after a positive result: P(D | +) = P(+ | D) × P(D) ÷ P(+).
Worked examples
Independent events with P(A) = 0.4 and P(B) = 0.3 give P(A and B) = 0.12 and P(A or B) = 0.58. In binomial mode, 10 trials with p = 0.2 give P(exactly 3) = 20.13% and P(at least 3) = 32.22%. For Bayes: a condition affects 1% of people, and the test catches 95% of cases but has a 5% false-positive rate. Out of 10,000 people, 95 true positives and 495 false positives test positive, so a positive result means only a 16.10% chance of the condition.
Checks
- Inconsistent inputs are flagged, for example P(A and B) bigger than P(A).
- Binomial results match SciPy on 200 random cases.
- This is a maths tool, not medical advice.
Frequently asked questions
What's the difference between independent and mutually exclusive?
Independent events don't affect each other's chances; mutually exclusive events can't both happen. Two events with non-zero chances can't be both.
Why is the Bayes answer so low?
When a condition is rare, the many healthy people produce more false positives than there are true positives. That's the base-rate effect.
Is the probability calculator free?
Yes. You can open the probability calculator and enter everything without signing up. When you calculate a probability for the first time, we ask once for your name and WhatsApp number; after that it, and every other Uncodemy tool, opens straight away.