Understanding Probability
Probability measures likelihood of an event occurring. P = favorable / total outcomes.
Key Formulas
| Type | Formula |
|---|---|
| Single Event | P(A) = favorable / total |
| Complement | P(not A) = 1 - P(A) |
| Independent AND | P(Aβ©B) = P(A) Γ P(B) |
| At least once (n trials) | 1 - (1-P)βΏ |
How to Use This Probability Calculator
Enter the number of favorable outcomes and total possible outcomes, or enter individual event probabilities. The calculator computes single event, combined (AND/OR), and conditional probabilities.
Formula & How It Works
P(A) = favorable / total. P(A and B) = P(A) Γ P(B) if independent. P(A or B) = P(A) + P(B) β P(A and B). Bayes: P(A|B) = P(B|A) Γ P(A) / P(B).
Calculation Example
Rolling two dice, P(sum=7) = 6/36 = 16.7%. P(at least one 6 in two rolls) = 1 β P(no 6)Β² = 1 β (5/6)Β² = 30.6%.
Expert Tips
The complement rule P(not A) = 1 β P(A) often simplifies calculations. "At least one" problems are best solved by 1 β P(none). Independent events: each roll/flip is unaffected by previous results.
Frequently Asked Questions
What is probability?
Probability = favorable outcomes / total outcomes. It ranges from 0 (impossible) to 1 (certain).
Independent vs dependent events?
Independent: P(A and B) = P(A) Γ P(B). Dependent: the outcome of A affects P(B).
What are odds vs probability?
Probability: 3 out of 10 = 30%. Odds: 3 to 7 (favorable to unfavorable).