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Express simple probability as a fraction

Probability of an event with equally likely outcomes is represented as a fraction: the numerator counts outcomes that meet the event, and the denominator counts all possible outcomes. The fraction expresses likelihood from 0 (impossible) to 1 (certain), and the denominator must represent the complete set of equally likely outcomes rather than merely the number of favorable outcomes. The scope is limited to simple, one-step situations, not compound, conditional, or theoretical probability.

Detailed Explanation: Express simple probability as a fraction

When all outcomes are equally likely, write probability as a fraction:

Probability=number of outcomes that fittotal number of possible outcomes\text{Probability}=\frac{\text{number of outcomes that fit}}{\text{total number of possible outcomes}}
  • The numerator (top number) counts the outcomes you want.
  • The denominator (bottom number) counts all possible outcomes.

Example: A bag has 5 marbles: 2 red marbles and 3 blue marbles. What is the probability of choosing a red marble?

  1. Count the outcomes that fit: There are 2 red marbles, so the numerator is 22.
  2. Count all possible outcomes: There are 5 marbles altogether, so the denominator is 55.
  3. Write the probability:
P(red)=25P(\text{red})=\frac{2}{5}

The probability of choosing a red marble is 25\frac{2}{5}. Remember to use the total number of possible outcomes for the denominator, not just the number of red marbles.

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