Probability Calculator Calculate single event, multiple events, and conditional probabilities — with step-by-step explana...
Probability Calculator
Calculate single event, multiple events, and conditional probabilities — with step-by-step explanations and real-world examples.
Single Event
Multiple Events
Conditional Probability
Probability Distributions
0.30
Probability
3:7
Odds
0.70
Complement
Single Event
Type
Probability Formulas
Basic Probability
P(E) = favorable/total
Complement
P(not E) = 1 - P(E)
Union
P(A∪B) = P(A) + P(B) - P(A∩B)
Conditional
P(A|B) = P(A∩B) / P(B)
Interpretation
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Probability Visualization
Probability Fundamentals
Probability is a measure of the likelihood that an event will occur, expressed as a number between 0 and 1.
Key Concepts**:
- Sample Space**: All possible outcomes of an experiment
- Event**: A specific outcome or set of outcomes
- Independent Events**: Occurrence of one doesn't affect the other
- Mutually Exclusive**: Events that cannot occur simultaneously
- Complementary Events**: Two events that are the only possible outcomes
Probability Rules**:
- 0 ≤ P(E) ≤ 1 for any event E
- P(impossible event) = 0
- P(certain event) = 1
- P(E) + P(not E) = 1
Common Probability Mistakes
⚠️ Avoid these critical errors:
- Gambler's Fallacy**: Believing past events affect future independent events
- Confusing P(A|B) with P(B|A)**: Base rate neglect in conditional probability
- Adding probabilities of non-mutually exclusive events**: Forgetting to subtract intersection
- Assuming independence**: When events are actually dependent
- Small sample sizes**: Drawing conclusions from insufficient data
✅ Best Practices**:
- Always define your sample space clearly
- Use tree diagrams for complex probability problems
- Apply Bayes' theorem for conditional probability problems
- Verify that probabilities sum to 1 in complete sample spaces
Real-World Applications
Probability is essential in:
- Finance**: Risk assessment, option pricing, portfolio management
- Medicine**: Diagnostic testing, clinical trials, epidemiology
- Weather Forecasting**: Precipitation probability, storm tracking
- Artificial Intelligence**: Machine learning algorithms, decision trees
- Quality Control**: Defect rate analysis, statistical process control
📊 Example Use Cases**:
- Medical testing**: False positive rate calculation using Bayes' theorem
- Investment risk**: Probability of portfolio loss exceeding threshold
- Manufacturing**: Probability of finding defective items in a batch
- Gambling**: Expected value calculation for casino games
How to Use This Calculator
➡️ Single Event
"3 favorable outcomes out of 10" → P = 0.3, Odds = 3:7
➡️ Multiple Events
"P(A)=0.3, P(B)=0.4, independent" → P(A OR B) = 0.58
➡️ Conditional Probability
"P(A)=0.3, P(B)=0.4, P(A AND B)=0.12" → P(A|B) = 0.3
➡️ Probability Distributions
"Binomial: n=10, p=0.5" → Mean=5, Variance=2.5
Note: All probabilities must be between 0 and 1. For dependent events, provide P(A AND B). Results are rounded to 4 decimal places for accuracy.