Conditional Probability Calculator
P(A|B) from P(A and B) and P(B).
Enter your values
Enter the p(a and b) you are working with.
Enter the p(b) you are working with.
Results update instantly as you type — no submit needed. Your values are remembered on this device, and the shareable link reopens the calculator with exactly these numbers.
- P(A | B)
- 50%
- P(A and B)
- 15%
- P(B)
- 30%
Quick answer
Conditional probability P(A|B) equals the probability of both A and B occurring, divided by the probability of B.
P(A|B) = P(A∩B)/P(B)
At a glance
| What it does | P(A|B) from P(A and B) and P(B). |
|---|---|
| Category | Statistics |
| Inputs needed | P(A and B), P(B) |
| Main output | P(A | B) |
| Formula | P(A|B) = P(A∩B)/P(B) |
| Cost | Free — no sign-up, no download |
How to use the Conditional Probability Calculator
- 1Enter the joint probability of both events A and B occurring.
- 2Enter the probability of the conditioning event B.
- 3Divide to get the conditional probability of A given B.
Inputs explained
- P(A and B)
- Enter the p(a and b) you are working with.
- P(B)
- Enter the p(b) you are working with.
Worked example
Using the values the calculator loads with:
Inputs
- P(A and B)0.15
- P(B)0.3
Results
- P(A | B)50%
- P(A and B)15%
- P(B)30%
Frequently asked questions
What if P(B) is zero?
Conditional probability is undefined since you can't condition on an impossible event.
How is this related to Bayes' theorem?
Bayes' theorem rearranges this same relationship to flip the condition around.
What do I need to enter into the Conditional Probability Calculator?
Just 2 values: p(a and b), p(b). Every field starts with a realistic example, so you can change one number at a time and watch the result update instantly.
How does the Conditional Probability Calculator work out the answer?
Conditional probability P(A|B) equals the probability of both A and B occurring, divided by the probability of B. It applies the formula P(A|B) = P(A∩B)/P(B) and shows the working so you can check each step by hand.
Is the Conditional Probability Calculator free, and do I need an account?
It is completely free with no sign-up, no download and no usage limit. Everything is calculated in your browser, so the numbers you type never leave your device.
Results are estimates for general information. For medical, legal, structural or financial decisions, confirm with a qualified professional.