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State the conditional probability formula.
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All Flashcards in Topic 4.11
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4.11.19 cards
State the conditional probability formula.
P(A | B) = P(A ∩ B) ÷ P(B).
What does P(A | B) mean?
The probability of A given that B has already occurred.
Which event do you divide by?
The given event — the one after the '|'.
If you only have P(A), P(B) and P(A ∪ B), how do you start?
Find P(A ∩ B) from the addition rule first.
From a two-way table, what is the denominator for P(A | B)?
The total of the given group B (e.g. all students), not the whole sample.
On a tree diagram, what kind of probability is a second-stage branch?
A conditional probability (given the first-stage outcome).
How do you reverse a condition on a tree (e.g. P(cause | effect))?
Use P(cause ∩ effect) ÷ P(effect), with P(effect) the total over all paths.
How is conditional probability linked to independence?
If P(A | B) = P(A), then A and B are independent.
Rearrange to find P(A ∩ B) from P(A | B) and P(B).
P(A ∩ B) = P(A | B) × P(B).
Topic 4.11 study notes
Full notes & explanations for Conditional probability
Math AA exam skills
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