1. What is Compound Probability?

Compound probability refers to the probability of two or more events occurring together. The formula P(A and B) = P(A) × P(B|A) calculates the probability that both events A and B occur, where P(B|A) is the probability of B given that A has already occurred.

2. How Does the Calculator Work?

The calculator uses the compound probability formula:

Where:

• \( P(A) \) — Probability of event A occurring
• \( P(B|A) \) — Conditional probability of event B occurring given that A has occurred

Explanation: This formula calculates the joint probability of two dependent events occurring in sequence.

3. Importance of Compound Probability

Details: Understanding compound probability is essential in statistics, risk assessment, decision making, and various fields including finance, insurance, and scientific research where multiple events interact.

4. Using the Calculator

Tips: Enter probabilities as values between 0 and 1. For example, 50% probability should be entered as 0.5. Both values must be valid probabilities.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between independent and dependent events?
A: For independent events, P(B|A) = P(B). For dependent events, the probability of B changes based on whether A occurred.

Q2: Can this formula be used for more than two events?
A: Yes, for multiple events: P(A and B and C) = P(A) × P(B|A) × P(C|A and B)

Q3: What if the events are mutually exclusive?
A: If events are mutually exclusive, they cannot occur together, so P(A and B) = 0.

Q4: How is this different from P(A or B)?
A: P(A or B) calculates the probability that at least one event occurs, while P(A and B) calculates the probability that both occur.

Q5: When should I use this formula?
A: Use this formula when you need to calculate the probability of multiple events occurring in sequence, particularly when the events are dependent on each other.