Random Number — Definition, Formula & Examples
A random number is a number selected from a set of possible values in such a way that each value has a known chance of being chosen, with no predictable pattern determining the outcome.
A random number is a numerical outcome generated by a random process, where the selection mechanism ensures that the probability of each possible value occurring conforms to a specified probability distribution and successive selections are independent of one another.
How It Works
Random numbers can be generated by physical methods like rolling a die or spinning a spinner, or by technology like a calculator's random function or a computer program. When you generate a random number between 1 and 10, each number should be equally likely to appear. The key property is unpredictability: knowing previous random numbers gives you no advantage in predicting the next one. In practice, computers use algorithms called pseudorandom number generators that produce sequences that behave like truly random numbers for most purposes.
Worked Example
Problem: You use a random number generator to pick a whole number from 1 to 6. What is the probability of getting a number greater than 4?
List outcomes: The possible random numbers are 1, 2, 3, 4, 5, and 6. Since the generator is random and uniform, each number is equally likely.
Identify favorable outcomes: Numbers greater than 4 are 5 and 6, giving 2 favorable outcomes out of 6 total.
Calculate the probability: Divide favorable outcomes by total outcomes.
Answer: The probability is , or about 0.333.
Why It Matters
Random numbers are essential for running simulations in science, conducting fair surveys, and designing games. In statistics courses and data science careers, generating random samples is the foundation for making trustworthy conclusions about large populations.
Common Mistakes
Mistake: Believing that after several high random numbers, a low number is "due" to appear.
Correction: Each random number is independent of previous ones. A fair generator has no memory, so past results do not influence future outcomes. This false belief is called the gambler's fallacy.