Calculate theoretical probability

Theoretical probability assigns a numerical likelihood to 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 includes representing outcomes with lists, tables, or tree diagrams, interpreting probabilities as fractions, decimals, or percentages, and using complements and simple compound events without assuming that observed experimental frequencies must match the theoretical value; conditional probability and more advanced counting methods are not included.

Detailed Explanation: Calculate theoretical probability

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

Use the formula

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

Example

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

Step 1: List all possible outcomes.

The die can land on

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: Substitute into the formula.

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

Step 4: Simplify and interpret.

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

So, the probability of rolling an even number is

\boxed{\frac{1}{2}}

or $0.5$ , or $50\%$ .

Theoretical probability is based on the possible outcomes. It does not mean that exactly half of a small number of rolls must be even; results can vary by chance.

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Probability Sample Space - Sample Space Definition and Favourable Outcomes Count to Probability

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