Maxi Calculator

Conditional Probability Calculator

Calculate the probability of events given other events have occurred

Conditional Probability Calculator

Enter the probability of event A occurring

Enter the probability of event B occurring

Enter the probability of both events A and B occurring

Table of Contents

How the Calculator Works

This calculator helps you find the probability of one event occurring given that another event has occurred:

  • Enter the probability of event A occurring, P(A)
  • Enter the probability of event B occurring, P(B)
  • Enter the probability of both events occurring together, P(A∩B)
  • The calculator will:
    • Calculate the conditional probability P(A|B)
    • Show the formula used
    • Break down the calculation steps
    • Display the final result as a percentage

Understanding Conditional Probability

Conditional probability measures the likelihood of an event occurring given that another event has already occurred:

  • The formula is:

    P(A|B) = P(A∩B) / P(B)

  • Key concepts:
    • P(A|B) reads as "probability of A given B"
    • P(A∩B) is the intersection (both events occurring)
    • Events can be dependent or independent
    • 0 ≤ P(A|B) ≤ 1 for all valid probabilities

Applications and Uses

Conditional probability has numerous practical applications:

  • Medical diagnosis and testing
  • Weather forecasting
  • Risk assessment
  • Quality control in manufacturing
  • Machine learning and AI
  • Insurance and actuarial science
  • Genetic studies

Frequently Asked Questions

What's the difference between P(A|B) and P(B|A)?

P(A|B) is the probability of A occurring given that B has occurred, while P(B|A) is the probability of B occurring given that A has occurred. These are generally different values unless the events are independent.

Why can't P(A∩B) be greater than P(A) or P(B)?

The probability of two events occurring together (intersection) cannot be greater than the probability of either event occurring individually. This is because the intersection is a subset of both individual events.

What happens if P(B) is zero?

If P(B) = 0, the conditional probability P(A|B) is undefined because it would involve division by zero. This makes sense intuitively because we can't condition on an impossible event.