Probability Calculator
Free probability calculator. Calculate the probability of single events, multiple independent events, and complement events with clear examples.
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Probability Calculator
P(Event) = Number of favorable outcomes ÷ Total possible outcomes
Probability
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Percentage
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Complement P(A')
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Comprehensive Guide & Practice
Master the mathematical principles, formulas, and step-by-step methods with worked examples and FAQs.
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1. What Is Probability?
Probability is a measure of how likely an event is to occur. It is always expressed as a number between 0 and 1, where 0 means the event is impossible and 1 means it is certain.
Formula: P(Event) = Number of favorable outcomes ÷ Total number of possible outcomes
Example: Rolling a 3 on a standard die: P(3) = 1/6 ≈ 0.1667 (16.67%).
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2. Types of Events
- Independent events: One event's outcome doesn't affect the other. P(A and B) = P(A) × P(B). Example: Flipping heads twice: 0.5 × 0.5 = 0.25 = 25%.
- Mutually exclusive events: Cannot both occur. P(A or B) = P(A) + P(B). Example: Rolling a 2 or 5 on a die: 1/6 + 1/6 = 1/3.
- Complementary events: P(not A) = 1 − P(A). Example: Probability of NOT rolling a 6: 1 − 1/6 = 5/6.
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3. Common Probability Examples
- Coin flip landing heads: 1/2 = 50%
- Rolling an even number on a die: 3/6 = 50%
- Drawing an ace from a deck of 52 cards: 4/52 = 7.69%
- Drawing a heart: 13/52 = 25%
See also: Combinations & Permutations | Statistics Calculator | Probability Basics Guide