Conditional Probability Calculator

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Introduction

Conditional Probability Calculator — Compute P(A|B) from P(A and B) and P(B). Enter P(A and B), P(B) to get an instant, accurate result.

Formula

P(A|B) = P(A and B) / P(B), the probability of A given that B has occurred.

Step-by-step

1. Enter the P(A and B).
2. Enter the P(B).
3. Click Calculate to see your result instantly.

Real-world example

Example: With P(A and B) = 0.2, P(B) = 0.5, the Conditional Probability Calculator gives P A Given B: 0.4.

Frequently Asked Questions

What if P(B) is zero?

Conditional probability is undefined when P(B) = 0, since an event with zero probability cannot be conditioned on.

How is this different from P(A and B)?

P(A and B) is the probability both happen out of all possible outcomes; P(A|B) narrows the sample space to only outcomes where B already happened.

What inputs does the Conditional Probability Calculator need?

You'll need to provide: P(A and B), P(B). All fields use sensible defaults, so you can see a working example immediately and then adjust the values to match your own numbers.

How accurate is the Conditional Probability Calculator?

The Conditional Probability Calculator applies the formula exactly as calculated — P(A|B) = P(A and B) / P(B), the probability of A given that B has occurred. — so results are precise for the inputs you provide. Accuracy depends on entering correct, realistic input values.

Is the Conditional Probability Calculator free to use?

Yes, the Conditional Probability Calculator is completely free, requires no signup, and runs instantly in your browser.

About the Conditional Probability Calculator

The Conditional Probability Calculator uses a real, verifiable formula — P(A|B) = P(A and B) / P(B), the probability of A given that B has occurred. — so results are accurate every time, not an approximation.