1. What is the 3-Way Probability Calculator?

The 3-Way Probability Calculator calculates the sum of three mutually exclusive probabilities (P1, P2, P3) that should theoretically sum to 1. It's useful for checking probability distributions in statistical analysis and probability theory.

2. How Does the Calculator Work?

The calculator uses the probability equation:

Where:

• \( P_1 \) — First probability (0 ≤ P1 ≤ 1)
• \( P_2 \) — Second probability (0 ≤ P2 ≤ 1)
• \( P_3 \) — Third probability (0 ≤ P3 ≤ 1)

Explanation: For mutually exclusive and exhaustive events, the sum of all probabilities should equal 1.

3. Importance of Probability Calculation

Details: Verifying that probabilities sum to 1 is essential in probability theory, statistical modeling, and decision analysis to ensure valid probability distributions.

4. Using the Calculator

Tips: Enter three probability values between 0 and 1. The calculator will sum them and show if they form a valid probability distribution (sum = 1).

5. Frequently Asked Questions (FAQ)

Q1: What if the sum doesn't equal 1?
A: If the sum ≠ 1, either the events aren't exhaustive, probabilities are incorrect, or there are additional unaccounted events.

Q2: Can I use this for more than 3 probabilities?
A: This calculator is specifically for 3 probabilities. For more probabilities, you would need to extend the equation.

Q3: What are valid probability ranges?
A: Each probability must be between 0 and 1 (0% to 100%).

Q4: What about non-mutually exclusive events?
A: For overlapping events, the calculation would need to account for intersections using the inclusion-exclusion principle.

Q5: How precise are the calculations?
A: Results are calculated to 4 decimal places, but rounding errors may occur with very small probabilities.