Probability Calculator
Likelihood of a specific outcome.
Formula first
Overview
This fundamental formula, known as classical probability, quantifies the likelihood of an event occurring within a finite sample space of equally likely outcomes. It establishes a ratio between the count of specific favorable results and the total count of all possible results in a trial.
Symbols
Variables
P = Probability, n(A) = Target Outcomes, n(S) = Total Outcomes
Apply it well
When To Use
When to use: Use this formula when dealing with discrete, finite sets where every individual outcome has an equal chance of occurring. It is the primary tool for analyzing outcomes in games of chance, basic statistical sampling, and initial risk modeling in data processing.
Why it matters: Calculating the ratio of specific outcomes to the total space allows for informed decision-making under uncertainty. It provides the mathematical framework for complex systems like insurance actuarial science, quality control, and machine learning classification.
Avoid these traps
Common Mistakes
- Result > 1.
- Reverse division.
One free problem
Practice Problem
A bag contains 8 blue marbles, 5 red marbles, and 7 green marbles. What is the probability of randomly picking a blue marble?
Solve for:
Hint: Divide the number of blue marbles by the total sum of all marbles in the bag.
The full worked solution stays in the interactive walkthrough.
References
Sources
- Wikipedia: Probability
- Britannica: Probability
- Ross, Sheldon M. A First Course in Probability, 8th ed.
- DeGroot, Morris H., and Mark J. Schervish. Probability and Statistics, 4th ed.
- Wikipedia: Classical definition of probability
- Standard curriculum — GCSE Mathematics (Probability)