Probability Calculatorv1.0.0

Calculate event probability with this online probability calculator. Enter the total outcomes and event counts to compute exact probabilities, complements, unions, intersections, and conditional probabilities. Analyze independent events, mutually exclusive events, and overlapping events to support statistics homework, classroom demonstrations, and everyday risk analysis.

• Compute P(A), P(A’), P(A∪B), P(A∩B), and P(A|B) from simple counts.
• Set relationships as mutually exclusive, not mutually exclusive, or independent to match real scenarios.
• Enter overlaps to resolve intersections precisely when events can occur together.
• Switch precision to format results for reports, assignments, and presentations.
• Start fast with presets for coin flips, dice rolls, and standard card decks.

Use this probability and statistics tool to improve understanding, check practice problems, and inform decisions where likelihood matters.

Use this online probability calculator to compute exact probabilities for single events and multiple events. Enter counts, set relationships, and read clear results with supporting formulas.

• Enter N, the total number of possible outcomes for your scenario.
• Enter k(A), k(B), and additional event counts that describe how many outcomes belong to each event.
• Click Add event to analyze more than one event or Remove event to simplify the setup.
• Open Advanced options and set the relationship between events as mutually exclusive, not mutually exclusive, or independent when needed.
• Provide an overlap count k(A∩B) when events are not mutually exclusive to resolve the intersection exactly.
• Press Calculate to view P(A), complements, unions, intersections, and conditional probabilities such as P(A|B).
• Change Decimal precision to format results for classwork, reports, or risk analysis.
• Apply Presets for coins, dice, or cards to start faster with common probability models.

Use whole numbers for counts, keep the sum of mutually exclusive event counts less than or equal to N, and supply overlaps only when events are not mutually exclusive.

Solve practical probability problems for study, teaching, and decision making. Translate raw counts into probabilities that guide planning and risk assessment.

• Verify homework by converting event counts into P(A), P(A’), P(A∪B), P(A∩B), and P(A|B).
• Teach statistics by demonstrating independent events, mutually exclusive events, complements, and conditional probability with instant feedback.
• Estimate business or project risk by modeling overlaps between triggers and outcomes to understand combined likelihood.
• Plan experiments by comparing theoretical probabilities to observed frequencies and refining sample sizes.
• Create study notes by copying formatted results and formulas for quick review before exams.

Cards: Model A as “draw a heart” and B as “draw a face card.” Enter N = 52, set k(A) = 13, k(B) = 12, choose “not mutually exclusive,” and enter the overlap k(A∩B) = 3 for heart face cards to compute P(A∪B) and P(A|B).

Quality control: Track A as “fails test 1” and B as “fails test 2” within a daily batch. Enter batch size for N, record failure counts for k(A) and k(B), and supply the overlap to estimate the chance that an item fails both tests and the conditional failure probability.

What is N? N is the total number of equally possible outcomes. Use the sample space size for coins, dice, cards, surveys, or batches.

When do I use independence? Use independence when one event does not affect the probability of the other. If outcomes influence each other, do not select independence.

How do I handle overlaps? Select “not mutually exclusive” and enter k(A∩B). The calculator then computes the union and conditional probabilities correctly.

Why do results show fractions and decimals? Fractions show exact ratios, and decimals provide readable values at the precision you choose. Both represent the same probability.