Probability Calculator

Calculate probabilities for single events, multiple events (AND/OR), conditional probability, and binomial distributions.

1. Single Event Probability

Favourable outcomes

Total outcomes

2. Multiple Events — AND / OR

P(Event A)

P(Event B)

Events are

Independent Mutually exclusive

3. Conditional Probability — P(A|B)

P(A and B)

P(B)

4. Binomial Probability — P(X = k)

Trials (n)

Successes (k)

P(success) per trial

Calculate

k	P(X=k)	P(X≤k)

Probability Fundamentals

Probability measures the likelihood of an event occurring, expressed as a number between 0 (impossible) and 1 (certain).

Key Rules

Rule	Formula
Complement	P(A') = 1 − P(A)
Addition (general)	P(A ∪ B) = P(A) + P(B) − P(A ∩ B)
Addition (mutually exclusive)	P(A ∪ B) = P(A) + P(B)
Multiplication (independent)	P(A ∩ B) = P(A) × P(B)
Conditional	P(A\|B) = P(A ∩ B) / P(B)
Bayes' Theorem	P(A\|B) = P(B\|A)×P(A) / P(B)

Binomial Distribution

P(X=k) = C(n,k) × pᵏ × (1−p)ⁿ⁻ᵏ, where C(n,k) = n! / (k!(n−k)!) is the binomial coefficient. Used when there are n independent trials, each with probability p of success.