Choose from Basic, Multiple Events, Conditional, Binomial, Dice, or Card probability
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Follow the step-by-step explanation to understand the method
Basic probability is the ratio of favorable outcomes to total outcomes. For multiple independent events: P(A and B) = P(A) × P(B). For any two events: P(A or B) = P(A) + P(B) - P(A and B). Conditional: P(A|B) = P(A and B) / P(B). Complement: P(A') = 1 - P(A).
P(A) = Favorable Outcomes / Total Outcomes
Probability is always between 0 (impossible) and 1 (certain) — or 0% to 100%
For independent events: P(A AND B) = P(A) × P(B)
For mutually exclusive events: P(A OR B) = P(A) + P(B)
For any two events: P(A OR B) = P(A) + P(B) − P(A AND B)
Complement rule: P(NOT A) = 1 − P(A) — always easier to find what you don't want
Binomial probability: use when you have n independent trials each with probability p
Probability is the mathematical language of uncertainty, quantifying how likely events are to occur on a scale from 0 (impossible) to 1 (certain). It underpins fields as diverse as insurance pricing, medical diagnosis, weather forecasting, quality control, gambling, and artificial intelligence. Basic probability is calculated as favorable outcomes divided by total possible outcomes — a fair six-sided die has a 1/6 probability (16.67%) of landing on any specific number. Conditional probability narrows the sample space: the probability of drawing a king given that you drew a face card is 4/12 or 33.3%, not 4/52. The binomial distribution models repeated independent trials — like the probability of getting exactly 7 heads in 10 coin flips (approximately 11.7%). Bayes' theorem, which combines prior probability with new evidence, is the foundation of modern statistical inference and machine learning classification. Understanding probability also prevents common reasoning errors: the gambler's fallacy (believing a coin is 'due' for heads after several tails), base rate neglect (ignoring how rare a condition is when interpreting test results), and the birthday paradox (in a group of just 23 people, there is a 50.7% chance two share a birthday). Whether you are evaluating risk, making business decisions under uncertainty, or solving statistics homework, probability provides the rigorous framework.
Probability quantifies how likely an event is to occur. It ranges from 0 (impossible) to 1 (certain). In everyday terms, a 0.5 probability means a 50-50 chance. Our calculator handles all standard probability types used in statistics, math, gambling analysis, and science.
Basic probability divides favorable outcomes by total outcomes. For multiple independent events, multiply probabilities (AND) or use the union formula (OR). Conditional probability asks 'what if we already know B happened?' Binomial probability handles repeated independent trials like flipping a coin n times.
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