MEPX
Chapter 2 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 2 of 11

Counting outcomes

Favourable over total.

The basic ratio

When outcomes are equally likely, the probability is the number of favourable ones divided by the total. One die has six faces and two of them beat 4, so the chance is 2 in 6, or 1 in 3.

  • A standard deck has 52 cards and 13 hearts, so drawing a heart is 1 in 4.
  • Listing outcomes is slow but never wrong. Use it to check a formula.

Equally likely matters

The ratio only works when every outcome has the same chance. Two dice have 11 possible totals but they are not equally likely, which is why you count the 36 combinations instead.