Probability Calculator (Independent, Conditional & Unions)
Calculates classical event probabilities, independent intersections P(A ∩ B), unions P(A ∪ B), and complements P(A').
1. Single Classical Event P(E) = n(E) / n(S)
2. Two Independent Events P(A) & P(B)
How This Calculation Formula is Formulated
Calculates classical Kolmogorov probability axioms for single random events, independent joint probabilities, and union probabilities.
Variable Definitions & Measurement Units
Rolling an Even Number on a 6-Sided Die
Finding probability of rolling 2, 4, or 6 on a fair standard die.
Independent vs Mutually Exclusive Events
Two events are independent if the occurrence of one does not alter the probability of the other: P(A ∩ B) = P(A) · P(B).
Two events are mutually exclusive if they cannot occur simultaneously: P(A ∩ B) = 0. Mutually exclusive events are NEVER independent (if one happens, the other cannot).
Frequently Asked Questions About Probability Calculator (Independent, Conditional & Unions)
What is the Gambler's Fallacy?
The mistaken belief that past independent events influence future trials (e.g. believing a coin is 'due' for heads after 5 tails). Each flip remains strictly 50% independent.
What is the complement rule in probability?
The probability of an event not occurring is P(A') = 1 − P(A).
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