1. What is Compound Event Probability?

Compound event probability calculates the likelihood of two independent events occurring together. For independent events A and B, the probability of both occurring is the product of their individual probabilities.

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)
• \( P(A \cap B) \) — Probability of both events occurring together

Explanation: This formula applies only when events A and B are independent (the occurrence of one does not affect the probability of the other).

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 as values between 0 and 1. For percentages, convert to decimal (e.g., 25% = 0.25). Ensure events are truly independent for accurate results.

5. Frequently Asked Questions (FAQ)

Q1: What defines independent events?
A: Events are independent if the occurrence of one does not affect the probability of the other occurring.

Q2: Can this formula be used for dependent events?
A: No, for dependent events use conditional probability: P(A ∩ B) = P(A) × P(B|A)

Q3: What if probabilities are given as percentages?
A: Convert percentages to decimals by dividing by 100 before calculation.

Q4: How many events can this handle?
A: This calculator handles two events. For more events, multiply all individual probabilities: P(A ∩ B ∩ C) = P(A) × P(B) × P(C)

Q5: What are some real-world applications?
A: Risk assessment, quality control, genetics, and predicting outcomes in games of chance.