Conditional Probability Calculator
Calculate the probability of events given other events have occurred
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
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
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
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.