1. What is Theoretical Probability?

Theoretical probability is the ratio of the number of favorable outcomes to the number of possible outcomes in an experiment. It's based on reasoning and mathematics rather than experimentation.

2. How Does the Calculator Work?

The calculator uses the theoretical probability formula:

Where:

• \( P \) — Probability of the event occurring
• Favorable Outcomes — Number of desired outcomes
• Total Possible Outcomes — Number of all possible outcomes

Explanation: The formula calculates the likelihood of an event occurring based on equally likely outcomes.

3. Importance of Probability Calculation

Details: Theoretical probability is fundamental in statistics, risk assessment, game theory, and decision-making processes across various fields.

4. Using the Calculator

Tips: Enter the number of favorable outcomes (must be ≥0) and total possible outcomes (must be >0 and ≥ favorable outcomes).

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between theoretical and experimental probability?
A: Theoretical probability is based on mathematical reasoning, while experimental probability is based on actual experiments or observations.

Q2: What are valid probability values?
A: Probability values range from 0 (impossible) to 1 (certain), often expressed as percentages (0% to 100%).

Q3: When is theoretical probability most accurate?
A: When all outcomes are equally likely and the sample space is well-defined (like fair dice, coins, or decks of cards).

Q4: What are common applications?
A: Games of chance, statistical sampling, quality control, weather forecasting, and risk assessment.

Q5: How does this differ from empirical probability?
A: Empirical probability is based on actual observations or historical data, while theoretical probability is based on theoretical models.