Pure & Applied MathematicsEntry № 03.12Documented FormulaVerified

Probability Calculator (Independent, Conditional & Unions)

Calculates classical event probabilities, independent intersections P(A ∩ B), unions P(A ∪ B), and complements P(A').

Probability & Axiomatic Events

1. Single Event: P(E) = n(E) / n(S)

Favorable n(E)

Sample Space n(S)

2. Compound Independent Events P(A) & P(B)

P(A) [0 - 1]

P(B) [0 - 1]

Single Event Probability P(E)

50%

Ratio: 0.5

P(A ∩ B) Joint15%

P(A ∪ B) Union65%

Event vs Complement

P(A ∪ B) = P(A) + P(B) − P(A ∩ B)

Popular Searches::How to calculate probability: favorable outcomes / total outcomesP(A or B) = P(A) + P(B) - P(A and B)Independent event multiplication rule

Mathematical Proof & FormulaStandard Mathematical Notation

How This Calculation Formula is Formulated

Calculates classical Kolmogorov probability axioms for single random events, independent joint probabilities, and union probabilities.

Standard Mathematical Notation

P(A) = n(E) / n(S) ; P(A ∪ B) = P(A) + P(B) − P(A ∩ B)

Documented algebraic formula with transparent derivation and reference notes.

Variable Definitions & Measurement Units

P(E)

Probability

Likelihood bounded between 0 (impossible) and 1 (certain).

n(E)

Favorable Outcomes

Count of target events.

n(S)

Sample Space

Total possible mutually exclusive outcomes.

Step-by-Step Calculation Example

Rolling an Even Number on a 6-Sided Die

Finding probability of rolling 2, 4, or 6 on a fair standard die.

Favorable Outcomes n(E)

{2, 4, 6} = 3 outcomes

Target events

Sample Space n(S)

{1, 2, 3, 4, 5, 6} = 6 outcomes

Total outcomes

Division

3 / 6 = 0.5000 (50%)

Probability

Conclusion: P(Even) = 0.50 (50.00% probability), with 1:1 odds in favor.

In-Depth Editorial Analysis

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

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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Deterministic Precision & 100% Client-Side Privacy

All calculations execute in your local browser using IEEE 754 double-precision floating-point arithmetic. Your figures and financial metrics remain private and are never uploaded or saved to any cloud servers.