Skill: Calculate theoretical probability

Explanation and Free Practice Resources

Theoretical probability assigns an event a value equal to the number of favorable outcomes divided by the total number of equally likely outcomes in a finite sample space, expressing the result as a fraction, decimal, or percentage. The understanding includes representing simple and compound events with organized lists, tables, or tree diagrams, and using complements or mutually exclusive cases appropriately; it excludes continuous probability models and advanced conditional-probability theory.

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Detailed Explanation: Calculate theoretical probability

Theoretical probability is found using

P(\text{event})=\frac{\text{number of favorable outcomes}}{\text{total number of equally likely outcomes}}.

Example: Two fair coins are tossed. What is the probability of getting exactly one head?

List all possible outcomes.
Each coin can show heads ( $H$ ) or tails ( $T$ ):

\{HH,\ HT,\ TH,\ TT\}

There are $4$ equally likely outcomes.

Identify the favorable outcomes.
Exactly one head occurs in:

\{HT,\ TH\}

There are $2$ favorable outcomes.

Use the probability formula.

P(\text{exactly one head})=\frac{2}{4}=\frac{1}{2}

Express the answer in other forms, if needed.

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

Therefore, the probability of getting exactly one head is $\boxed{\frac{1}{2}}$ , or $\boxed{50\%}$ .

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

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