MEPX
Chapter 4 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 4 of 11

Dependent events

When the pool changes.

Without replacement

Drawing without putting the card back changes the second draw. Four aces in 52 cards, then three aces in the remaining 51, and multiplying gives 1 in 221.

  • With replacement, the second draw is unchanged and the answer differs.
  • Always ask whether the first event removed something.

Chains

For several dependent draws, multiply the chances step by step, adjusting the pool each time. Writing the fractions in a row makes the cancellation obvious.