Probability Calculator · Practical guide
How to Calculate Conditional Probability
When event B depends on event A, chain the probabilities: P(A and B) = P(A) × P(B | A).
At a glance
The Formula
Conditional probability handles events that influence each other. The probability that both happen is P(A AND B) = P(A) × P(B | A), where P(B | A) — read "probability of B given A" — is the chance of B after A has already occurred.
Interactive tool
Probability Calculator
Enter your own values, then compare the result with the examples below.
A Worked Example
Suppose there is a 30% chance of rain tomorrow, and if it rains, a 50% chance the game is canceled. The overall chance of a rainout is P(A) × P(B | A) = 0.30 × 0.50 = 0.15 — a 15% probability. Enter those two numbers in the Conditional tab above to get the same result.
Solving Backward
The same formula rearranges to recover the conditional probability when you know the joint and the base: P(B | A) = P(A AND B) ÷ P(A). If 15% of all days are both rainy and canceled, and 30% of days are rainy, then P(cancel | rain) = 0.15 ÷ 0.30 = 0.50.
Conditional vs Independent
When events are independent, knowing A happened tells you nothing about B, so P(B | A) simply equals P(B) and the formula collapses to the ordinary product rule. Conditional probability is the general tool; independence is the special case where the condition does not matter.
Frequently Asked Questions
What does the | symbol mean?
It means "given." P(B | A) is the probability that B occurs under the condition that A has already occurred.
Is P(B | A) the same as P(A | B)?
Almost never. The chance of rain given clouds is high; the chance of clouds given rain is nearly certain. Swapping the condition changes the meaning entirely.
Can a conditional probability exceed P(A and B)?
Yes — it usually does. P(B | A) divides the joint probability by P(A), a number at most 1, so the conditional value is at least as large as the joint one.
Where is conditional probability used in real life?
Medical test accuracy, weather forecasting, spam filtering, and insurance pricing all rely on it — anywhere the odds of one thing change once you know another.