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What does Bayes' theorem do?
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All Flashcards in Topic 4.13
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4.13.18 cards
What does Bayes' theorem do?
It reverses a conditional probability: turns P(evidence | cause), which you usually know, into P(cause | evidence), which you usually want.
State the conditional-probability formula behind Bayes.
P(A | B) = P(A ∩ B) / P(B) — the joint probability of the wanted branch over the total probability of the condition.
State Bayes' theorem (two-event form).
P(A | B) = [P(B|A)P(A)] / [P(B|A)P(A) + P(B|A′)P(A′)].
What is the law of total probability for an event B?
P(B) = P(B|A)P(A) + P(B|A′)P(A′) — sum the probability of B over every branch.
How do you build the denominator in a Bayes problem?
Add up every path on the tree that ends in the observed evidence (the total probability of the evidence).
Why can P(disease | positive) be small even with a 95%-accurate test?
If the disease is rare, the many false positives from the large healthy group outnumber the few true positives, so a positive result is often a false alarm.
What's the most common Bayes mistake?
Confusing P(A | B) with P(B | A) — the whole point of Bayes is that these two are different.
How does Bayes change with three causes A₁, A₂, A₃?
The denominator becomes P(B|A₁)P(A₁) + P(B|A₂)P(A₂) + P(B|A₃)P(A₃); the method (wanted branch ÷ total) is unchanged.
Topic 4.13 study notes
Full notes & explanations for Bayes' theorem (HL only)
Math AA exam skills
Paper structures, command terms & tips
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