1. What is Compound Probability?

Compound probability refers to the probability of two independent events both occurring. It's calculated by multiplying the probabilities of the individual events when they are independent of each other.

2. How Does the Calculator Work?

The calculator uses the compound probability formula:

Where:

• \( P \) — Compound probability (dimensionless)
• \( P(A) \) — Probability of event A (0 to 1)
• \( P(B) \) — Probability of event B (0 to 1)

Explanation: The formula assumes events A and B are independent (the occurrence of one doesn't affect the probability of the other).

3. Importance of Compound Probability

Details: Understanding compound probability is essential in statistics, risk assessment, and decision-making processes where multiple independent factors contribute to an outcome.

4. Using the Calculator

Tips: Enter probabilities for both events as values between 0 and 1. For example, 0.5 for 50% probability. The calculator will compute the probability of both events occurring.

5. Frequently Asked Questions (FAQ)

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

Q2: How does this differ from conditional probability?
A: Conditional probability calculates the chance of an event given that another event has occurred, while compound probability of independent events simply multiplies their individual probabilities.

Q3: Can this formula be used for dependent events?
A: No, for dependent events you would need to use conditional probability: P(A and B) = P(A) × P(B|A).

Q4: What's an example of compound probability?
A: The probability of flipping a coin and getting heads (0.5) and rolling a die to get a 6 (1/6) is 0.5 × 1/6 = 0.0833 or 8.33%.

Q5: How do you handle more than two events?
A: For independent events, simply multiply all individual probabilities: P(A and B and C) = P(A) × P(B) × P(C).