Determine theoretical probability

Theoretical probability describes the likelihood of an event by comparing the number of favorable outcomes with the total number of equally likely outcomes in a finite sample space: $P(E)=\frac{\text{favorable outcomes}}{\text{total outcomes}}$ . It can be represented as a fraction, decimal, or percent, including the probability of a complement, and requires distinguishing theoretical likelihood from experimental results; this treatment excludes conditional probability and more advanced probability models.

Detailed Explanation: Determine theoretical probability

Theoretical probability tells how likely an event is when all outcomes are equally likely.

Use the formula

P(E)=\frac{\text{number of favorable outcomes}}{\text{total number of possible outcomes}}.

Example

A fair six-sided die is rolled. What is the probability of rolling an even number?

Step 1: List all possible outcomes.

A die can show

1,2,3,4,5,6

There are $6$ total outcomes.

Step 2: Identify the favorable outcomes.

The even numbers are

2,4,6

There are $3$ favorable outcomes.

Step 3: Use the probability formula.

P(\text{even})=\frac{3}{6}

Step 4: Simplify and represent the answer in other forms.

\frac{3}{6}=\frac{1}{2}=0.5=50\%

So, the theoretical probability of rolling an even number is

\boxed{\frac{1}{2},\text{ or }0.5,\text{ or }50\%}.

This is a theoretical probability because it is based on the possible outcomes of a fair die. The actual results from rolling a die many times may not be exactly $(50\%)$ .

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Probability - Dice (3), All Same, To Fraction

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