Probability Calculator
Calculate probabilities for single events, complements, and multiple events. Perfect for statistics, gaming, and decision-making.
Enter Probability Data
Provide the number of favorable and total outcomes
The number of outcomes that satisfy your condition
The total number of possible outcomes
Choose the type of probability calculation you need
Probability Results
Calculated probability values
Enter your probability data and click "Calculate Probability" to see your results
Common Probability Examples
Real-world probability scenarios
Simple Events
Coin flip (heads)50%
Dice roll (6)16.67%
Card draw (Ace)7.69%
Birthday match (23 people)50.7%
Multiple Events
Two coin heads25%
Two dice sum = 716.67%
At least one 6 in two dice30.56%
Royal flush in poker0.000154%
About Probability
What is Probability?
Probability is the measure of the likelihood that an event will occur. It is quantified as a number between 0 and 1, where 0 indicates impossibility and 1 indicates certainty. The higher the probability of an event, the more likely it is that the event will occur.
Basic Probability Formula
P(A) = Number of Favorable Outcomes / Total Number of Outcomes
Where:
- • P(A) = Probability of event A
- • Number of Favorable Outcomes = outcomes that satisfy the condition
- • Total Number of Outcomes = all possible outcomes
Types of Probability Calculations
Single Event
- • Probability of one specific event
- • Basic probability formula
- • Example: P(rolling a 6) = 1/6
Complement
- • Probability of event NOT occurring
- • P(not A) = 1 - P(A)
- • Example: P(not 6) = 5/6
Independent Events
- • Events that don't affect each other
- • P(A and B) = P(A) × P(B)
- • Example: P(two heads) = 1/2 × 1/2 = 1/4
Dependent Events
- • Events that affect each other
- • P(A and B) = P(A) × P(B|A)
- • Example: Drawing cards without replacement
Probability Representations
- Percentage: Most common representation (e.g., 50%)
- Decimal: Mathematical representation (e.g., 0.5)
- Fraction: Exact representation (e.g., 1/2)
- Odds: Ratio of success to failure (e.g., 1:1)
- Ratio: Comparison of favorable to total outcomes
Applications of Probability
- Statistics: Foundation for statistical analysis and inference
- Finance: Risk assessment, insurance calculations, investment analysis
- Games: Casino games, sports betting, game theory
- Science: Quantum mechanics, genetics, experimental design
- Engineering: Quality control, reliability analysis, risk assessment
- Medicine: Drug effectiveness, disease prevalence, diagnostic tests
- Weather: Forecasting, climate modeling, risk assessment
Important Probability Concepts
- Sample Space: Set of all possible outcomes
- Event: Subset of the sample space
- Mutually Exclusive: Events that cannot occur simultaneously
- Exhaustive: Events that cover all possible outcomes
- Conditional Probability: Probability of A given B has occurred
- Bayes' Theorem: Updates probabilities based on new information
- Expected Value: Long-term average of repeated trials
Tips for Using This Calculator
- Ensure favorable outcomes ≤ total outcomes
- Both values must be non-negative integers
- For multiple events, provide data for both events
- Independent events don't affect each other's probability
- Dependent events require conditional probability calculations
- The complement is always 100% minus the original probability
- Use the fraction form for exact probability representation