1. What is Joint Probability?

Joint probability refers to the probability of two events occurring together. For independent events, the joint probability is simply the product of their individual probabilities.

2. How Does the Calculator Work?

The calculator uses the joint 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 applies only to independent events where the occurrence of one event does not affect the probability of the other.

3. Importance of Joint Probability

Details: Joint probability is fundamental in probability theory and statistics. It's used in risk assessment, decision making, and various fields including finance, insurance, and scientific research.

4. Using the Calculator

Tips: Enter probabilities as values between 0 and 1. For example, 25% probability should be entered as 0.25. Both probabilities must be valid (between 0 and 1).

5. Frequently Asked Questions (FAQ)

Q1: What if events are not independent?
A: This calculator assumes independent events. For dependent events, you would need to use conditional probability: P(A and B) = P(A) × P(B|A).

Q2: Can I use percentages instead of decimals?
A: The calculator requires decimal values between 0 and 1. Convert percentages by dividing by 100 (e.g., 25% = 0.25).

Q3: What does a result of 0 mean?
A: A result of 0 means the events cannot occur together (impossible outcome).

Q4: What does a result of 1 mean?
A: A result of 1 means the events are certain to occur together.

Q5: Can I calculate for more than two events?
A: For independent events, you can extend the formula: P(A and B and C) = P(A) × P(B) × P(C).