Quiz 2

Chatty reference · stats1 week 8

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2026-08-16T00:00:00.000Z
Python Week 1: the first filter for runtime behavior
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ChatGPT archive slice for week 8. # 28.

28. Stats W8 — Conditional Probability

This is probably one of the highest-value Quiz 2 areas.
Concepts:
  • Conditional probability
  • Multiplication rule
  • Independence
  • Law of total probability
  • Bayes' theorem
Definition:
P(AB)=P(AB)P(B)P(A\mid B) = \frac{P(A\cap B)}{P(B)}
Multiplication:
P(AB)=P(AB)P(B)P(A\cap B) = P(A\mid B)P(B)
Independence:
P(AB)=P(A)P(B)P(A\cap B)=P(A)P(B)
or equivalently:
P(AB)=P(A)P(A\mid B)=P(A)
when applicable.
Bayes:
P(AB)=P(BA)P(A)P(B)P(A\mid B) = \frac{P(B\mid A)P(A)} {P(B)}

The pattern we're going to hammer

A question gives you:
evidence BB
and asks:
probability of underlying condition AA.
That is often a Bayesian inversion problem.

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