Probability Calculator

Compute probabilities of events using basic probability rules and Bayes' theorem with detailed step-by-step solutions!

About Probability Calculator

Welcome to our Probability Calculator, a powerful tool designed to compute the probabilities of different events using basic probability rules and Bayes' theorem. This calculator is ideal for students, teachers, and anyone working with probability and statistics.

Features of the Probability Calculator

Step-by-Step Solutions: Understand each step involved in computing probabilities.
Visualization: Graphically represent probabilities with simple charts.
Comprehensive Results: Supports basic probability calculations, conditional probability, and Bayes' theorem.
User-Friendly Interface: Input probabilities easily and get instant results.
Accurate Computations: Ensures precise calculations using fundamental probability formulas.

Understanding Basic Probability Concepts

Probability quantifies the likelihood of an event occurring and ranges from 0 (impossible) to 1 (certain).

Basic Probability

For any two events \( A \) and \( B \), the probability of \( A \cup B \) (either \( A \) or \( B \) occurring) is given by:

\[ P(A \cup B) = P(A) + P(B) - P(A \cap B) \]

If \( A \) and \( B \) are mutually exclusive (cannot occur simultaneously), then:

\[ P(A \cup B) = P(A) + P(B) \]

Conditional Probability

The probability of event \( A \) occurring given that event \( B \) has occurred is called the conditional probability of \( A \) given \( B \), denoted by \( P(A|B) \), and is calculated as:

\[ P(A|B) = \frac{P(A \cap B)}{P(B)} \]

Bayes' Theorem

Bayes' theorem relates the conditional and marginal probabilities of events \( A \) and \( B \):

\[ P(A|B) = \frac{P(B|A) \times P(A)}{P(B)} \]

How to Use the Probability Calculator

Select the type of probability problem you want to solve from the dropdown menu.
Enter the required probabilities for the selected problem type.
Click on "Compute Probability" to process your inputs.
View the probability result along with step-by-step solutions and graphs.

Why Use Our Probability Calculator?

Calculating probabilities manually can be complex and time-consuming. Our calculator simplifies the process by providing:

Accuracy: Ensuring precise calculations using fundamental probability formulas.
Efficiency: Saving time on homework, tests, or professional projects.
Educational Value: Enhancing understanding through detailed steps and visual aids.