Random — Definition, Formula & Examples
Random means that an outcome cannot be predicted with certainty before it happens. When something is random, each possible result occurs without a deliberate pattern or bias.
A process or selection is random if every eligible outcome has a well-defined probability of occurring, and no individual outcome can be determined in advance. In a simple random process, each outcome is equally likely.
How It Works
A process is random when you cannot know the result ahead of time, even if you know all the possible outcomes. Flipping a fair coin is random because you know the outcomes are heads or tails, but you cannot predict which one will land. Randomness is essential for fair experiments and surveys because it prevents bias from influencing the results. Over many trials, random outcomes tend to follow predictable patterns described by probability.
Worked Example
Problem: A bag contains 5 red marbles and 5 blue marbles. You reach in without looking and draw one marble. Is this selection random, and what is the probability of drawing a red marble?
Check for randomness: You cannot see the marbles, so you have no way to choose a specific color. Every marble has an equal chance of being selected, making this a random process.
Find the probability: There are 5 red marbles out of 10 total marbles.
Answer: Yes, the selection is random. The probability of drawing a red marble is , or 50%.
Why It Matters
Random sampling is the foundation of polls, medical studies, and quality testing — any time you need results that fairly represent a larger group. In your math classes, understanding randomness is the first step toward calculating probabilities and designing experiments that produce trustworthy data.
Common Mistakes
Mistake: Thinking random means completely chaotic with no patterns at all.
Correction: Individual random outcomes are unpredictable, but over many trials the results follow reliable probability patterns. For example, a fair coin lands on heads about 50% of the time over thousands of flips.