What is a Probability Calculator?
This calculator helps you solve probability problems, including combinations, permutations, conditional probability, and basic probability operations for statistics and mathematics.
This calculator helps you solve probability problems, including combinations, permutations, conditional probability, and basic probability operations for statistics and mathematics.
How to Use Probability Calculations
- Combinations C(n,r): Number of ways to choose r items from n items when order doesn't matter.
- Permutations P(n,r): Number of ways to arrange r items from n items when order matters.
- Conditional Probability P(A|B): Probability of A occurring given that B has occurred.
- Union P(A∪B): Probability that either A or B (or both) occurs.
- Intersection P(A∩B): Probability that both A and B occur.
- Complement P(A'): Probability that A does not occur (1 - P(A)).
Example: To calculate C(10,3), enter the values in the quick input form or use the C(n,r) button and enter "10,3".
How to Use the Probability Calculator
- Use the calculator buttons to build probability expressions or enter values directly.
- Click function buttons like C(n,r) for combinations or P(n,r) for permutations.
- Use the quick input forms for faster calculations of common probability functions.
- Press "=" to calculate. Use "C" to clear the display.
Probability Theory Basics
- Sample Space: The set of all possible outcomes of an experiment.
- Event: A subset of the sample space.
- Probability: A number between 0 and 1 representing the likelihood of an event.
- Independent Events: Events where the occurrence of one doesn't affect the other.
- Mutually Exclusive: Events that cannot occur at the same time.
Common Probability Formulas
- Basic Probability: P(A) = Number of favorable outcomes / Total number of outcomes
- Combination: C(n,r) = n! / (r!(n-r)!)
- Permutation: P(n,r) = n! / (n-r)!
- Conditional Probability: P(A|B) = P(A∩B) / P(B)
- Addition Rule: P(A∪B) = P(A) + P(B) - P(A∩B)
- Multiplication Rule: P(A∩B) = P(A) × P(B|A)
Probability in Real Life
- Risk assessment in finance and insurance
- Quality control in manufacturing
- Medical diagnosis and treatment planning
- Weather forecasting and climate modeling
- Game theory and decision making
Frequently Asked Questions about Probability
Combinations count selections where order doesn't matter (choosing 3 people from 10). Permutations count arrangements where order matters (arranging 3 people in a line from 10).
Conditional probability P(A|B) = P(A and B) / P(B). It's the probability of A happening given that B has already occurred.
P(A∪B) is the union probability - the chance that either event A or event B (or both) will occur. Formula: P(A∪B) = P(A) + P(B) - P(A∩B).