AND Probability Calculator
Enter P(A) and P(B), choose an assumption (independent events or custom joint probability), and evaluate P(A ∩ B).
P(A ∩ B): 0.2400
P(A | B): 0.6000
P(B | A): 0.4000
How to Use This Calculator
- Enter the probabilities of events A and B.
- Select whether the events are independent or if you have a known P(A ∩ B).
- Review the joint probability and conditional probabilities P(A | B) and P(B | A).
- Use the results to solve probability problems involving intersections and conditionals.
Formula
Independent events: P(A ∩ B) = P(A) × P(B)
General case: P(A ∩ B) provided by user
Conditional: P(A | B) = P(A ∩ B) / P(B), P(B | A) = P(A ∩ B) / P(A)
Full Description
The intersection probability represents the likelihood that events A and B occur simultaneously. Under independence, it equals the product of marginal probabilities. When independence is not assumed, the user can supply P(A ∩ B) directly to compute related conditional probabilities.
Frequently Asked Questions
What if I don’t know P(A ∩ B)?
If you assume independence, the calculator uses P(A) × P(B). Otherwise, obtain the joint probability from data or context.
Why must P(A ∩ B) ≤ min(P(A), P(B))?
Intersections cannot exceed the probability of either event. The calculator warns when this condition is violated.
Are probabilities limited to two events?
Yes. For more events, extend the concept iteratively or use advanced probability rules.
Can I enter percentages?
Inputs are fractions between 0 and 1. Convert percentages by dividing by 100.