Math & Engineering
Probability Calculator
Calculate the probability of events occurring using different probability methods.
Enter values to calculate probability
Related to Probability Calculator
The probability calculator helps you determine the likelihood of events occurring using different probability calculation methods. It supports three main types of probability calculations: single events, multiple independent events, and conditional probability.
Single Event Probability
For a single event, probability is calculated by dividing the number of favorable outcomes by the total number of possible outcomes. The formula is P(E) = (favorable outcomes) / (total outcomes). For example, the probability of rolling a 6 on a die is 1/6.
Multiple Independent Events
When calculating the probability of multiple independent events occurring together, we multiply the individual probabilities. For n identical events, we raise the single event probability to the power of n. The formula is P(E₁∩E₂) = P(E₁) × P(E₂) for different events, or P(E)ⁿ for n identical events.
Conditional Probability
Conditional probability calculates the likelihood of an event occurring given that another event has already occurred. The formula is P(A∩B) = P(A) × P(B|A), where P(B|A) is the probability of B occurring given that A has occurred.
The calculator provides results as both decimal probabilities and percentages, along with the mathematical formula used. Understanding these results helps in making informed decisions based on probability.
Probability Scale
Probability is always expressed as a number between 0 and 1 (or 0% to 100%): - 0 (0%) means the event is impossible - 1 (100%) means the event is certain - 0.5 (50%) means the event has an equal chance of occurring or not occurring
Result Interpretation
The explanation provided with each calculation shows the step-by-step process and the formula used. This helps you understand how the final probability was determined and verify the calculation's accuracy.
1. What is probability?
Probability is a measure of the likelihood of an event occurring. It is expressed as a number between 0 and 1, where 0 represents impossibility and 1 represents certainty. Probability theory provides a mathematical framework for analyzing random phenomena and making predictions about future events.
2. How do I calculate the probability of getting at least one success?
To calculate the probability of at least one success, first calculate the probability of no successes and subtract it from 1. For example, if you roll a die three times looking for at least one 6, calculate: 1 - (5/6)³. This is known as the complement rule of probability.
3. What's the difference between independent and dependent events?
Independent events are events where the occurrence of one event does not affect the probability of the other event occurring. For example, when flipping a coin twice, each flip is independent. Dependent events are events where the first event affects the probability of the second event, like drawing cards from a deck without replacement.
4. Can probability be negative or greater than 1?
No, probability cannot be negative or greater than 1. Probability is always expressed as a number between 0 and 1 (inclusive). This is because probability represents the proportion of favorable outcomes to total possible outcomes, which cannot be negative or exceed the total number of possibilities.
5. What is the scientific source for this calculator?
This calculator is based on fundamental probability theory principles established in mathematical statistics. The formulas and methods used are derived from classical probability theory, first formalized by Pierre-Simon Laplace in his 1812 work "Théorie analytique des probabilités." The calculations follow standard probability axioms defined by Andrey Kolmogorov in his 1933 book "Foundations of the Theory of Probability." These principles are widely accepted in mathematics and statistics and are used in various fields including science, engineering, and data analysis.