Conditional probability

P(A|B)=\dfrac{P(A\cap B)}{P(B)}

Result unit: — ($\langle 0,1\rangle$)

What it describes

The probability that event A occurs given that B has occurred.

P(A|B)

conditional probability

P(A\cap B)

probability of the intersection

P(B)

probability of the condition (

>0

)

When we know that B has occurred, the sample space narrows to B — so we divide by

P(B)

. It answers the question "what is the probability of A, given that B has occurred".

Dependent events, successive draws without replacement, stochastic trees.

P(A\cap B)=0.2

P(B)=0.5

. Find

P(A|B)

Substitution

\dfrac{0.2}{0.5}

Result

P(A|B)=0.4

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