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Theoretical and Experimental Probability

Key Questions

  • Answer:

    determine the number of winning outcomes and losing outcomes then divide each by the total number of outcomes.

    Explanation:

    If there are 4 chances of winning and 10 possible outcomes then the odds of winning are 4/10 or 2/4

    If there are 5 chances of winning and 10 possible outcomes then the odd of losing are 5/10 = 1/2

    It is possible that some outcomes are neutral and do not result in either winning or losing In this example 1/10

  • Theoretical Probability

    Assume that each outcome is equally likely to occur.

    Let #S# be a sample space (the set of all outcomes), and let #E# be an event (a subset of #S#).

    The probability of the event #E# can be found by

    #P(E)={n(E)}/{n(S)}#,

    where #n(E)# and #n(S)# denote the number of outcomes in #E# and the number of outcomes in #S#, respectively.


    Example

    What is the probability of rolling a multiple of 3 when you roll a standard die once?

    Since all outcomes are 1 through 6, we have the sample space

    #S={1,2,3,4,5}#

    Since all multiple of 3 are 3 and 6, we have the event

    #E={3,6}#

    Hence, the probability of rolling a multiple of 3 is

    #P(E)={n(E)}/{n(S)}=2/6=1/3#


    I hope that this was helpful.

Questions