Probability Calculator - Calculate Event Probabilities
Calculate probabilities for single events, multiple independent/dependent events, conditional probability, and complements with results shown as fractions, decimals, and percentages
Probability Calculator
Result
Select probability type and click Calculate
What is a Probability Calculator?
A Probability Calculator is a free mathematical tool that helps you calculate the likelihood of events occurring. It supports single events, multiple independent and dependent events, conditional probability, and complement probability with results displayed as fractions, decimals, and percentages.
This calculator is perfect for:
- Students - Learn and verify probability concepts for homework and exams
- Statisticians - Perform quick probability calculations for data analysis
- Educators - Demonstrate probability principles with interactive examples
- Researchers - Calculate event probabilities for experiments and studies
For analyzing binomial probability distributions with multiple trials, explore our Binomial Distribution Calculator to calculate probabilities for discrete random variables.
To measure data variability and spread, use our Standard Deviation Calculator to understand how values deviate from the mean.
For testing statistical significance and independence, check our Chi-Square Calculator to perform hypothesis testing on categorical data.
How Probability Calculations Work
The calculator uses fundamental probability formulas based on the calculation type:
Key Probability Concepts
Sample Space
The set of all possible outcomes of an experiment. For a die roll, the sample space is 6.
Event
A subset of the sample space. For example, rolling an even number is the event 6.
Independence
Two events are independent if the occurrence of one doesn't affect the probability of the other.
Mutual Exclusivity
Events that cannot occur simultaneously. Rolling a 2 and rolling a 5 are mutually exclusive.
How to Use This Calculator
Select Probability Type
Choose from single, independent, dependent, conditional, or complement
Enter Values
Input probabilities or outcomes based on selected type
Calculate Result
Click Calculate to compute the probability
View Multiple Formats
See results as fraction, decimal, and percentage
Benefits of Using This Calculator
- • Multiple Formats: View results as fractions, decimals, and percentages for easy understanding.
- • Comprehensive Coverage: Support for single, independent, dependent, conditional, and complement probabilities.
- • Educational Value: Learn probability concepts with formula displays and instant calculations.
- • Accurate Results: Precise calculations following standard probability theory principles.
- • Time-Saving: Quickly verify homework solutions or perform statistical analyses.
Important Probability Rules
1. Probability Range
All probabilities must be between 0 and 1 (or 0% to 100%). Values of 0 indicate impossibility, and 1 indicates certainty.
2. Sum of Probabilities
The sum of all possible outcomes in a sample space equals 1. An event and its complement always sum to 1.
3. Independence Matters
For independent events, multiply probabilities. For dependent events, use conditional probability formulas.
4. Valid Inputs Required
Ensure favorable outcomes don't exceed total outcomes, and conditional probabilities use valid joint and marginal values.
Frequently Asked Questions (FAQ)
Q: What is probability and how is it calculated?
A: Probability is the measure of the likelihood of an event occurring. It is calculated as the number of favorable outcomes divided by the total number of possible outcomes. Probability values range from 0 (impossible) to 1 (certain), and can be expressed as fractions, decimals, or percentages.
Q: What is the difference between independent and dependent events?
A: Independent events are events where the occurrence of one does not affect the probability of the other (like flipping two coins). Dependent events are events where the occurrence of one affects the probability of the other (like drawing cards without replacement).
Q: What is conditional probability?
A: Conditional probability is the probability of an event occurring given that another event has already occurred. It is denoted as P(A|B) and calculated as P(A and B) / P(B), representing the probability of A given that B has happened.
Q: What is complement probability?
A: Complement probability is the probability that an event does NOT occur. It is calculated as 1 - P(A), where P(A) is the probability of the event occurring. The sum of an event's probability and its complement always equals 1.