Sample Space, Favorable Outcomes and Formula for Theoretical Probability

Theoretical probability, as discussed earlier, is calculated without even performing the experiment. It is calculated based on the sample space and the number of favorable outcomes out of that sample space. What is sample space then?

Sample Space

Sample space is the collection of all possible outcomes or results from an experiment. It is thus useful to list the sample space of an experiment, because it helps you calculate the total number of possible outcomes of an experiment. The following examples of sample space will illustrate it clearly.

Favorable Outcomes

In simple words, a "Favorable Outcome" is the desired result of an experiment. For example, you toss and coin and want heads, then getting heads is a favorable outcome, whereas getting tails is not a favorable outcome.


Find the favorable outcomes to getting an even number when rolling a dice.

A dice has six faces, numbered 1 through 6. The even numbers on it are 2, 4 and 6. Thus, there are three favorable outcomes out of total six possible outcomes when rolling a dice.

Formula for Theoretical Probability

Theoretical probability is calculated solely on the basis of the sample space and the number of outcomes in the sample space that meet the condition required in any given question. Its formula is:
`P("outcome") = "Number of Favorable Outcomes"/"Total Number of Possible Outcomes"`
The "outcome" written in parenthesis after 'P' represents the particular outcome for which the probability is being calculated. For example, if you are calculating the probability of getting the number 3 when throwing a dice, then you would write 3 in place of "outcome", that is, you will write P(3).

The number of favorable outcomes in the above formula are the same as discussed above, that is, the number of outcomes out of the sample space that match the given condition in the question.

The total number of possible outcomes is the total number of outcomes listed in the sample space. For example, for throwing two dice, the total number of possible outcomes is 36.

It would serve better to further your knowledge of probability by solving, or seeing how they are solved, some simple questions on probability (that apply the above formula).

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