What Is Probability?
Probability is a measure of the likelihood that an event will occur, expressed as a number between 0 and 1. A probability of 0 means the event is impossible, and a probability of 1 means the event is certain. For example, a fair coin has a 0.5 probability of landing heads.
Probability theory forms the mathematical foundation for statistics, data science, gambling, insurance, and decision-making under uncertainty. Understanding how to combine probabilities of multiple events is essential for solving real-world problems.
Key Probability Formulas
Probability Rules Summary
| Rule | Formula | When to Use |
|---|---|---|
| Addition Rule | P(A∪B) = P(A)+P(B)-P(A∩B) | Either A or B occurs |
| Multiplication (Independent) | P(A∩B) = P(A)×P(B) | Both A and B occur (independent) |
| Complement | P(A') = 1 - P(A) | Event A does not occur |
| Conditional | P(A|B) = P(A∩B)/P(B) | A occurs given B occurred |
Frequently Asked Questions
What does "independent events" mean?
Two events are independent if the occurrence of one does not affect the probability of the other. For example, flipping a coin and rolling a die are independent. Drawing cards without replacement from a deck are dependent events because each draw changes the remaining probabilities.
Can probability be negative?
No. Probability values are always between 0 and 1 (inclusive). If a calculation yields a negative number, it indicates an error in the input values or an impossible scenario (e.g., P(A∩B) greater than P(A) or P(B)).