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Write probability as a fraction

Probability is represented as a fraction comparing the number of favorable outcomes with the total number of equally likely outcomes in a finite sample space; the numerator identifies outcomes that satisfy the event and the denominator counts all possible outcomes. The fraction may be simplified without changing its value, and probabilities range from 0 (impossible) to 1 (certain); conditional probability and non-equally likely outcomes are beyond this scope.

Detailed Explanation: Write probability as a fraction

To write a probability as a fraction, use:

Probability=number of favorable outcomestotal number of possible outcomes\text{Probability}=\frac{\text{number of favorable outcomes}}{\text{total number of possible outcomes}}
  • Favorable outcomes are the results you want.
  • Total possible outcomes are all the equally likely results.

Example: What is the probability of rolling an even number on a fair six-sided die?

  1. List all possible outcomes: 1,2,3,4,5,61,2,3,4,5,6.
  2. Count the total outcomes: there are 66.
  3. Identify the favorable outcomes. The even numbers are 2,4,62,4,6, so there are 33 favorable outcomes.
  4. Write the fraction:
36\frac{3}{6}
  1. Simplify the fraction by dividing the numerator and denominator by 33:
36=12\frac{3}{6}=\frac{1}{2}

So, the probability of rolling an even number is 12\boxed{\frac{1}{2}}. A probability is always between 00 and 11, including 00 and 11.

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