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Conditional probability P(A|B) is the probability of event A occurring, given that event B has already occurred. It updates your probability estimate based on new information.
Formula: P(A|B) = P(A ∩ B) / P(B), where P(A ∩ B) is the probability that both A and B occur, and P(B) > 0.
Example — a bag contains 4 red and 6 blue marbles. You draw one marble (not replaced) and it's red. What is the probability the second draw is also red? P(2nd red | 1st red) = 3/9 = 1/3 ≈ 33.3%. Without knowing the first draw, P(red) = 4/10 = 40%.
Conditional probability is the foundation of Bayes' theorem, medical test interpretation, spam filters, and machine learning classifiers. Understanding it helps avoid the base-rate fallacy and the prosecutor's fallacy.
P(A|B) = P(A ∩ B) / P(B)
This calculator is for educational purposes only and does not constitute professional advice. Results are based on standard mathematical formulas. Always verify critical calculations with a qualified professional before making important decisions.