Probability Calculator
Calculate basic probability, conditional probability, joint probability, and union probability with step-by-step solutions.
Calculator
Select a calculation type and enter the required values to calculate probabilities with step-by-step solutions.
Probability
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Step-by-Step Solution
Complete User Guide
What is Probability?
Probability is a measure of the likelihood that an event will occur. It ranges from 0 (impossible) to 1 (certain), or 0% to 100%.
Probability Types
- Basic Probability P(A): P(A) = Favorable outcomes / Total outcomes
- Conditional Probability P(A|B): Probability of A given B: P(A|B) = P(A and B) / P(B)
- Joint Probability P(A and B): Probability of both A and B: P(A and B) = P(A) × P(B) for independent events
- Union Probability P(A or B): Probability of A or B (or both): P(A or B) = P(A) + P(B) - P(A and B)
Key Concepts
- Independent Events: Events where the occurrence of one does not affect the other
- Dependent Events: Events where the occurrence of one affects the probability of the other
- Mutually Exclusive: Events that cannot occur simultaneously (P(A and B) = 0)
Examples
Example 1: Basic Probability
Problem: Rolling a 6 on a die
Favorable: 1
Total: 6
Result: P(6) = 1/6 ≈ 0.1667 or 16.67%
Example 2: Joint Probability
Problem: Rolling two 6s (independent events)
P(6 on first): 1/6
P(6 on second): 1/6
Result: P(6 and 6) = (1/6) × (1/6) = 1/36 ≈ 0.0278