MEPX
Chapter 5 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 5 of 11

Complements and at least one

Work from the opposite side.

One minus the rest

The chance of an event and the chance of it not happening add to 1. Questions asking for at least one are much easier as one minus the chance of none.

  • Two flips give no head only once in four, so at least one head is 3 in 4.
  • Ten flips with no head at all is 1 in 1024.

The birthday problem

In a room of 23 people the chance that two share a birthday passes one half, which surprises everyone. It is calculated as one minus the chance that all birthdays differ.