Probability Calculator - Event Probability Probability Calc
Enter probabilities for events A and B to calculate complement, union, intersection, and conditional probability.
Event Probabilities
Your Results
P(A ∪ B) — Either A or B 0.72
Formula P(A) + P(B) − P(A ∩ B) = 0.6 + 0.3 − 0.18 = 0.72
P(A) 0.6
P(B) 0.3
P(A') — Complement of A 0.4
P(B') — Complement of B 0.7
P(A ∩ B) — Both A and B 0.18
P(A ∪ B) — Either A or B 0.72
P(A | B) — A given B 0.6
P(B | A) — B given A 0.3
P(A' ∩ B') — Neither A nor B 0.28
Independent? Yes
Mutually Exclusive? No
Probability Calculator - Guide
What is Probability?
Probability is a numerical measure of the likelihood that an event will occur. It ranges from 0 (impossible) to 1 (certain). For example, a fair coin has P(heads) = 0.5.
Key Formulas
1. Complement
P(A') = 1 − P(A)
2. Union (Addition Rule)
P(A ∪ B) = P(A) + P(B) − P(A ∩ B)
3. Intersection
Independent: P(A ∩ B) = P(A) × P(B)
General: P(A ∩ B) = P(A|B) × P(B)
4. Conditional Probability
P(A | B) = P(A ∩ B) ÷ P(B)
5. Bayes' Theorem
P(A | B) = [P(B | A) × P(A)] ÷ P(B)
Independent vs Mutually Exclusive
- Independent: One event does not affect the other. P(A ∩ B) = P(A) × P(B).
- Mutually Exclusive: Both events cannot happen at the same time. P(A ∩ B) = 0.
Examples
- Coin flip: P(heads) = 0.5, P(tails) = 0.5, P(heads ∪ tails) = 1.
- Dice: P(rolling 6) = 1/6 ≈ 0.1667. P(rolling even) = 3/6 = 0.5.
- Cards: P(ace) = 4/52 ≈ 0.0769. P(heart) = 13/52 = 0.25.
How This Calculator Works
- Enter P(A) and P(B): Probabilities from 0 to 1.
- Optional P(A ∩ B): If left blank, events are assumed independent.
- Get results: Complement, union, intersection, conditional probability, and event relationship checks.
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