Probability Calculator
This calculator computes basic probabilities using fundamental rules. Enter probabilities for events A and B, and the calculator shows P(A), P(not A), P(A or B), and P(A and B) for independent events. Probability is the foundation of statistics and risk analysis, essential for decision-making under uncertainty.
Probability rules
P(not A) = 1 - P(A)
P(A and B) = P(A) * P(B) [for independent events]
P(A or B) = P(A) + P(B) - P(A and B)
P(A and not B) = P(A) * (1 - P(B))
Key concepts
- Complement: P(not A) is the opposite of event A.
- Intersection (and): Both events occur together.
- Union (or): At least one event occurs.
- Independence: One event does not affect the other.
Independent events, and the gambler's fallacy
Most probability mistakes come from mixing up independent and dependent events. A coin has no memory: after nine heads the tenth flip is still an even chance, because each flip is independent, and the belief that a tail is now 'due' is the gambler's fallacy that has funded casinos for centuries. Dependent events are the opposite. Drawing a card without replacing it changes what remains, so the odds shift with every draw, and treating them as independent quietly distorts the real chance.
Two more traps recur. The probability of 'A and B' multiplies only when the events are independent, while 'A or B' adds the two but must then subtract the overlap you would otherwise count twice. And rare-event intuition is poor: even a highly accurate test for a rare condition produces many false positives, because a small percentage of a large healthy group can outnumber the genuine cases, which is why a single positive result is always read alongside how common the condition actually is.
Probability: frequently asked questions
What is probability?
Probability is the likelihood of an event occurring, expressed as a number between 0 and 1. P = 0 means impossible, P = 1 means certain. P = 0.5 means equally likely.
What is P(A and B) for independent events?
For independent events: P(A and B) = P(A) * P(B). The events do not influence each other.
What is P(A or B)?
P(A or B) = P(A) + P(B) - P(A and B). We subtract P(A and B) to avoid double-counting when both occur.
How do I find P(not A)?
P(not A) = 1 - P(A). The complement of an event is everything except that event.
Official sources
- NIST/SEMATECH e-Handbook: NIST Handbook.
Reviewed by the CalculatorHub team, edited by James Graham, 14 June 2026. See our methodology.