How this calculator works
Conditioning restricts the sample space to outcomes where B occurs. The joint probability measures the part of that restricted set where A also occurs. No independence assumption is required. The joint probability cannot exceed P(B). Solving backward for P(B) needs a positive conditional probability; zero divided by zero would leave many possible answers.
Formula
P(A | B) = P(A and B)/P(B). P(A and B) = P(A | B)P(B). P(B) = P(A and B)/P(A | B), when the divisor is positive.
Worked example
If 20% of all outcomes satisfy A and B, and 50% satisfy B, then P(A | B) = 0.20/0.50 = 40%. Conversely, P(A | B) = 40% and P(B) = 25% give a joint probability of 10%.
Advertisement
Frequently asked questions
Does conditioning assume independence?
No. If A and B are independent, conditioning leaves P(A) unchanged, but the definition works without that assumption.
Can P(B) equal zero?
This elementary conditional-probability formula is undefined when P(B) is zero, so the calculator rejects it.
Can I infer P(B | A) from these inputs?
You also need P(A) to reverse the conditioning. Bayes theorem is useful when the relevant prior and likelihoods are available.