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Determine theoretical probability

Theoretical probability describes the likelihood of an event based on a finite sample space and assumptions about equally likely outcomes, calculated as the ratio of favorable outcomes to total possible outcomes and expressed as a fraction, decimal, or percent. It includes simple and familiar compound events, complements, and interpreting probabilities from tables, lists, or diagrams, while distinguishing theoretical predictions from experimental results; continuous probability and advanced probability models are not included.

Detailed Explanation: Determine theoretical probability

Theoretical probability predicts how likely an event is by assuming all outcomes are equally likely.

Use the formula

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

Example: What is the theoretical probability of rolling a number greater than 44 on a fair six-sided die?

  1. List the possible outcomes.
    A six-sided die can land on

1,2,3,4,5,6.1,2,3,4,5,6.

There are 66 total possible outcomes.

  1. Identify the favorable outcomes.
    The numbers greater than 44 are

5 and 6.5 \text{ and } 6.

There are 22 favorable outcomes.

  1. Substitute into the formula.

P(rolling greater than 4)=26.P(\text{rolling greater than }4)=\frac{2}{6}.

  1. Simplify and express the probability.

26=13=0.333…≈33.3%.\frac{2}{6}=\frac{1}{3}=0.333\ldots\approx 33.3\%.

So, the theoretical probability is 13\boxed{\frac{1}{3}}, or about 33.3%\boxed{33.3\%}.

This is a prediction based on equally likely outcomes. The results from actually rolling the die may not be exactly 33.3%33.3\%, especially if you only roll it a small number of times.

Learn by doing: Determine theoretical probability

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

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