The probability calculator solves basic probability problems: single event probability, AND/OR compound events, complement, and repeated trials. Enter favorable and total outcomes, or direct probabilities.
Probability Calculator
How to Use the Probability Calculator
Probability measures how likely an event is to occur, ranging from 0 (impossible) to 1 (certain). This calculator handles three common probability types.
Single Event
P(event) = favorable outcomes / total outcomes. Rolling a 4 on a die: 1/6 ≈ 0.167 = 16.7%. Drawing a heart from a deck: 13/52 = 0.25 = 25%. The complement P(not A) = 1 − P(A).
Compound Events (A AND/OR B)
For independent events: P(A AND B) = P(A) × P(B). P(A OR B) = P(A) + P(B) − P(A AND B). For mutually exclusive events (can't both happen): P(A OR B) = P(A) + P(B).
Repeated Trials (Binomial)
P(exactly k successes in n trials) = C(n,k) × p^k × (1-p)^(n-k). For 3 heads in 5 fair coin flips: C(5,3) × 0.5³ × 0.5² = 10 × 0.125 × 0.25 = 0.3125 = 31.25%.
FAQ
What is probability?
Probability measures likelihood of an event, from 0 (impossible) to 1 (certain). P = favorable outcomes / total outcomes. A fair die: P(rolling 3) = 1/6 ≈ 0.167 = 16.7%. A fair coin: P(heads) = 1/2 = 50%.
What is the difference between AND and OR probability?
P(A AND B) = P(A) × P(B) for independent events. P(A OR B) = P(A) + P(B) − P(A AND B). Example: P(rain AND cold) = 0.3 × 0.4 = 0.12. P(rain OR cold) = 0.3 + 0.4 − 0.12 = 0.58. If events are mutually exclusive, P(A OR B) = P(A) + P(B).
Is this calculator free?
Yes, completely free with no signup required. All calculations run in your browser.
Is my data private?
Yes. All calculations run locally. Nothing is transmitted.
What is the complement rule?
P(A') = 1 − P(A). The probability of an event NOT occurring equals 1 minus the probability it does occur. If P(rain) = 0.3, then P(no rain) = 0.7. Useful for 'at least one' problems: P(at least one head in 3 flips) = 1 − P(no heads) = 1 − (0.5)³ = 0.875.