1. What is Conditional Probability?

Conditional probability is the probability of an event occurring given that another event has already occurred. It's a fundamental concept in probability theory and statistics, widely used in various fields including machine learning, medical testing, and risk assessment.

2. How Does the Calculator Work?

The calculator uses the conditional probability formula:

Where:

• \( P(A|B) \) — Probability of event A occurring given that B is true
• \( P(A \cap B) \) — Probability of both A and B occurring
• \( P(B) \) — Probability of event B occurring

Explanation: The formula calculates how the probability of A changes when we know that B has occurred.

3. Importance of Conditional Probability

Details: Conditional probability is essential for understanding dependent events, Bayesian statistics, and making predictions based on partial information. It's used in medical diagnosis (test accuracy), weather forecasting, and financial risk modeling.

4. Using the Calculator

Tips: Enter the probability of both events occurring (must be between 0 and the probability of B) and the probability of event B (must be between 0 and 1). Both values must be valid probabilities.

5. Frequently Asked Questions (FAQ)

Q1: What if P(B) is zero?
A: Conditional probability is undefined when P(B) = 0, as you can't condition on an impossible event.

Q2: How is this different from joint probability?
A: Joint probability P(A∩B) is the probability of both events occurring, while conditional probability P(A|B) is the probability of A given that B has occurred.

Q3: Can conditional probability be greater than 1?
A: No, conditional probability must be between 0 and 1, like all probabilities.

Q4: What's the relationship with Bayes' Theorem?
A: Bayes' Theorem is derived from the definition of conditional probability and allows reversing the conditionality.

Q5: When is P(A|B) equal to P(A)?
A: When A and B are independent events, P(A|B) = P(A).