1. What is Compound Probability?

Compound probability calculates the likelihood of two independent events both occurring. The formula P(A and B) = P(A) × P(B) applies when events A and B are independent, meaning the occurrence of one doesn't affect the probability of the other.

2. How Does the Calculator Work?

The calculator uses the compound probability formula:

Where:

• \( P(A) \) — Probability of event A occurring (0 to 1)
• \( P(B) \) — Probability of event B occurring (0 to 1)

Explanation: This formula multiplies the individual probabilities of two independent events to find the probability that both events occur together.

3. Importance of Compound Probability

Details: Compound probability is essential in statistics, risk assessment, game theory, and decision-making processes where multiple independent factors influence outcomes.

4. Using the Calculator

Tips: Enter probabilities between 0 and 1. For percentages, convert to decimal (e.g., 25% = 0.25). Ensure events are independent for accurate results.

5. Frequently Asked Questions (FAQ)

Q1: What makes events independent?
A: Events are independent if the occurrence of one event doesn't affect the probability of the other event occurring.

Q2: What if events are not independent?
A: For dependent events, use conditional probability: P(A and B) = P(A) × P(B|A)

Q3: Can probabilities be greater than 1?
A: No, probabilities range from 0 (impossible) to 1 (certain). Compound probability will always be ≤ the smaller individual probability.

Q4: How to convert percentages to probabilities?
A: Divide percentage by 100 (e.g., 75% = 0.75, 20% = 0.20)

Q5: What are some real-world applications?
A: Risk assessment, quality control, weather forecasting, game strategies, and financial modeling.