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Calculate theoretical probability

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.

Detailed Explanation: Calculate theoretical probability

Theoretical probability is found using

P(event)=number of favorable outcomestotal number of equally likely outcomes.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?

  1. List all possible outcomes.
    Each coin can show heads (HH) or tails (TT):

{HH, HT, TH, TT}\{HH,\ HT,\ TH,\ TT\}

There are 44 equally likely outcomes.

  1. Identify the favorable outcomes.
    Exactly one head occurs in:

{HT, TH}\{HT,\ TH\}

There are 22 favorable outcomes.

  1. Use the probability formula.

P(exactly one head)=24=12P(\text{exactly one head})=\frac{2}{4}=\frac{1}{2}

  1. Express the answer in other forms, if needed.

12=0.5=50%\frac{1}{2}=0.5=50\%

Therefore, the probability of getting exactly one head is 12\boxed{\frac{1}{2}}, or 50%\boxed{50\%}.

Learn by doing: Calculate theoretical probability

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

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