Probability Calculator — Joint, Union & Conditional Event
Compute joint (A∩B), union (A∪B), conditional P(A|B), and complement probabilities for independent or mutually exclusive events with Venn diagram.
Probability
Results below
Enter Values
P(A)
0.5
P(B)
0.3
P(¬A) — Probability of Not A
0.5
P(¬B) — Probability of Not B
0.7
P(A|B) — Conditional Probability of A given B
▲ 0.5
P(B|A) — Conditional Probability of B given A
▲ 0.3
P(A) as %
50.0%
P(B) as %
30.0%
Event Type
Independent
Scenario Comparison
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P(A)
0.5
50.0%
P(B)
0.3
30.0%
P(A ∩ B)
0.15
15.0%
P(A ∪ B)
0.65
65.0%
P(¬A) — Not A
0.5 (50.0%)
P(¬B) — Not B
0.7 (70.0%)
P(A|B) — A given B
0.5 (50.0%)
Independent: P(A|B) = P(A)
Relationship
Independent
Events do not affect each other
Venn Diagram
Why Independent Events?
Independent events have no influence on each other. The occurrence of B does not change the probability of A, so P(A|B) = P(A). The joint probability is the product: P(A ∩ B) = P(A) × P(B).
Examples: Flipping a coin and rolling a die; drawing two cards with replacement; weather in two different cities on the same day (approximately).
The addition rule for independent events: P(A ∪ B) = P(A) + P(B) − P(A)P(B). The overlap P(A ∩ B) is subtracted to avoid double-counting.
Calculation Breakdown
P(A ∩ B) — Intersection
P(A∩B) = P(A) × P(B) = 0.5 × 0.3 = 0.15
P(A ∪ B) — Union
P(A∪B) = P(A) + P(B) − P(A∩B) = 0.5 + 0.3 − 0.15 = 0.65
Complements
P(¬A) = 1 − 0.5 = 0.5
P(¬B) = 1 − 0.3 = 0.7
P(A|B) — Conditional
Independent: P(A|B) = P(A) = 0.5
Key Rules Summary
Addition Rule
P(A∪B) = P(A) + P(B) − P(A∩B)
Multiplication Rule
P(A∩B) = P(A) × P(B) (independent)
Complement Rule
P(¬A) = 1 − P(A)
Conditional Probability
P(A|B) = P(A∩B) ÷ P(B)
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