MEPX
Chapter 8 of 11All chapters
  1. 1What probability means
  2. 2Counting outcomes
  3. 3Independent events
  4. 4Dependent events
  5. 5Complements and at least one
  6. 6Adding probabilities
  7. 7Permutations and combinations
  8. 8Conditional probability
  9. 9Expected value
  10. 10Distributions in outline
  11. 11Fallacies and traps

Chapter 8 of 11

Conditional probability

The chance of one thing given another.

Narrowing the pool

Given that a card is a face card, the chance it is a king is 4 in 12. Conditioning throws away the outcomes that no longer apply and rescales the rest.

  • Written P(A given B), and it is usually not the same as P(B given A).
  • Confusing the two directions is behind most medical test misunderstandings.

Bayes in words

Start with how common something is, then update with how strong the evidence is. A rare condition plus a good test can still leave the odds against, because the starting point matters.