Properties of a Binomial Experiment

Key Questions

  • In a Binomial setting, there are only two possible outcomes per try. Depending on what you want, you call one of the possibilities Fail and the other one Succes.

    Example :
    You may call rolling a 6 with a die Succes, and a non-6 a Fail. Depending on the conditions of the game, rolling a 6 may cost you money, and you may want to reverse the terms.

    In short:
    There are only two possible outcomes per try, and you may name them as you want: White-Black, Heads-Tails, whatever.
    Usually the one you use as #P# in calculations is called (probability of) Succes.

  • In a BInomial setting there are two possible outcomes per event.

    The important conditions for using a binomial setting in the first place are:

    • There are only two possibilities, which we will call Good or Fail
    • The probability of the ratio between Good and Fail doesn't change during the tries
    • In other words: the outcome of one try does not
      influence the next

    Example :
    You roll dice (one at a time) and you want to know what the chances are that you roll at lest 1 six in 3 tries.
    This is a typical example of binomial:

    • There are only two possibilities:
      6 (chance #=1/6#) or not-6 (chance #=5/6#)
    • The die has no memory, so:
    • Every next roll has still the same probabilities.

    You can set up a chance-tree, but you can also calculate the chance of three Fails, which is


    And your chance of succeeding would be