Statistics · Probability
Chapter 1 · 4
The idea
Conditional probability
The probability of A given B, P(A|B) = P(A ∩ B) / P(B), as restricting the sample space to B — reading it off a Venn diagram, the multiplication formula P(A ∩ B) = P(B)P(A|B), and testing independence with P(A|B) = P(A).
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Statistics · Probability
Conditional probability
The probability of A given B, P(A|B) = P(A ∩ B) / P(B), as restricting the sample space to B — reading it off a Venn diagram, the multiplication formula P(A ∩ B) = P(B)P(A|B), and testing independence with P(A|B) = P(A).
Why it works
A smaller world
"What's the chance the match is cancelled?" is one question. "What's the chance it's cancelled, given that it's raining?" is a different — usually bigger — one. Conditional probability asks: given that one event has already happened, how likely is another? Written — "the probability of given " — it measures within the new, smaller world where is known to have occurred.B becomes the sample space
That "smaller world" is the whole idea. Once you know has happened, the only outcomes still possible are those in , so becomes the new sample space. The chance of is then the slice of that also lies in : On a Venn diagram this is simply (the overlap) ÷ (the whole of ) — you ignore everything outside .Keep reading — free
The rest of the explanation, plus 3 worked examples you step through move by move.
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