Counting > Possibilities
1234Possibilities

Theory

A number of tools are available to systematically count the number of outcomes :

  • The road diagram:
    This is a diagram (a graph) showing the options as connecting lines between points. The number of lines between points corresponds to the number of options. You get the total number of outcomes by multiplying the number of options from point to point.
  • The tree diagram:
    A diagram in which all options are shown as branches from a starting point.
    This tree diagram has two "levels". The first level has 2 branches and the second level has 3 branches.

  • Writing out the possible outcomes systematically:
    There are six ways to get two "heads" (H) and two "tails" (T) when tossing four coins: HHTT, HTHT, HTTH, THHT, THTH, TTHH.

  • A grid:
    This grid shows the equally probable outcomes when tossing two coins.

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