1. What is Joint Probability of 3 Events?

The joint probability of three independent events A, B, and C is the probability that all three events occur simultaneously. For independent events, this is simply the product of their individual probabilities.

2. How Does the Calculator Work?

The calculator uses the probability multiplication rule:

Where:

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

Explanation: This formula only applies when all three events are independent (the occurrence of one doesn't affect the others).

3. Importance of Joint Probability

Details: Calculating joint probabilities is fundamental in probability theory, statistics, risk assessment, and decision making. It helps determine the likelihood of multiple conditions being true simultaneously.

4. Using the Calculator

Tips: Enter probabilities for each event (must be between 0 and 1). The calculator will compute their joint probability. All values must be valid probabilities.

5. Frequently Asked Questions (FAQ)

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

Q2: What does a joint probability of 0.5 mean?
A: It means there's a 50% chance that all three events will occur together.

Q3: Can I use percentages instead of decimals?
A: You can, but you'd need to convert them to decimals first (e.g., 25% = 0.25).

Q4: What's the difference between joint and conditional probability?
A: Joint probability is the chance of multiple events happening together, while conditional probability is the chance of one event given that another has occurred.

Q5: Why does multiplying probabilities give a smaller number?
A: Because you're calculating the chance of multiple events all happening, which is always less likely than any single event occurring alone.