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Conditional probability

Probability · Formula · Not yet linked from a lesson

Probability

P(A \mid B) = \frac{P(A \cap B)}{P(B)}

Narrows the world to the cases where B happened, then asks how often A happens inside it. Independence is exactly the case where this narrowing changes nothing.

Symbols

$A \cap B$: The event that both A and B occur.
$P(B)$: The probability of the condition, which must not be zero.

Appears in

No lesson links this one yet. The roadmaps are filling in wave by wave.

Bayes' theorem $P(A \mid B) = \frac{P(B \mid A)\, P(A)}{P(B)}$
Law of total probability $P(A) = \sum_{i} P(A \mid B_i)\, P(B_i)$

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