Probability Calculator | Bayes
Solve compound event probabilities, unions, intersections, Bayes
Union P(A ∪ B)65.00%
Intersection P(A ∩ B)15.00%
Venn Diagram Overlap Visualization
Interactive Venn circles represent event space. Purple region outlines intersection set P(A ∩ B).
Step-by-step Mathematical Workings
Since A and B are Independent:
P(A ∩ B) = P(A) × P(B) = 0.5 × 0.3 = 0.1500
Calculate Union (At least one occurs):
P(A ∪ B) = P(A) + P(B) − P(A ∩ B)
P(A ∪ B) = 0.5 + 0.3 − 0.1500 = 0.6500
Calculate Complements (Non-occurrence):
P(A') = 1 − P(A) = 0.5000
P(B') = 1 − P(B) = 0.7000
Calculate Conditionals:
P(A|B) = P(A ∩ B) / P(B) = 0.1500 / 0.3 = 0.5000
P(B|A) = P(A ∩ B) / P(A) = 0.1500 / 0.5 = 0.3000