Probability Calculator
Calculate single event, AND, OR, and conditional probabilities. Enter all values between 0 and 1.
Probability Formulas Reference
| Formula | Meaning | Condition |
|---|---|---|
| P(not A) = 1 − P(A) | Complement of A | Always |
| P(A and B) = P(A) × P(B) | Both events occur | Independent events |
| P(A or B) = P(A) + P(B) − P(A∩B) | At least one occurs | General rule |
| P(A or B) = P(A) + P(B) | At least one occurs | Mutually exclusive |
| P(A|B) = P(A∩B) / P(B) | A given B occurred | P(B) > 0 |
Frequently Asked Questions
What is probability?
Probability is a measure of how likely an event is to occur, expressed as a number between 0 and 1 (or 0% to 100%). A probability of 0 means the event is impossible; a probability of 1 means it is certain. For example, the probability of a fair coin landing heads is 0.5 (50%).
What is P(A and B)?
P(A and B) is the probability that both event A and event B occur. For independent events (where one does not affect the other), P(A and B) = P(A) × P(B). For example, the probability of rolling a 6 on two separate dice = 1/6 × 1/6 = 1/36 ≈ 2.78%.
What is P(A or B)?
P(A or B) is the probability that at least one of event A or event B occurs. The formula is P(A or B) = P(A) + P(B) − P(A and B). We subtract P(A and B) to avoid counting it twice. For mutually exclusive events (where both cannot happen simultaneously), P(A and B) = 0, so P(A or B) = P(A) + P(B).
What is conditional probability P(A|B)?
P(A|B) is the probability of event A occurring given that event B has already occurred. The formula is P(A|B) = P(A and B) / P(B). For example, if P(rain) = 0.3, P(carry umbrella) = 0.4, and P(rain and carry umbrella) = 0.25, then P(rain | carry umbrella) = 0.25 / 0.4 = 0.625 (62.5%).
What are independent vs dependent events?
Two events are independent if the occurrence of one does not affect the probability of the other. Rolling two dice or flipping two coins are classic independent events. Events are dependent if knowledge of one changes the probability of the other. Drawing cards from a deck without replacement creates dependent events.