Practice Randomness in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

Quick Recap

Randomness is the quality of having no predictable pattern at the individual level, yet following precise probability rules over many repetitions — outcomes are uncertain one at a time but statistically regular in the long run.

Truly random means you can't predict the next outcome, even with complete information.

Example 1

easy
A coin is flipped 10 times and lands heads every time. A student says 'the next flip must be tails.' Explain why this is incorrect (the Gambler's Fallacy) using the concept of randomness.

Example 2

medium
A random number generator produces: 3, 7, 1, 9, 2, 8, 5, 4, 6, 10 (each number 1-10 equally likely). Explain what 'truly random' means and distinguish it from 'looking random.'

Example 3

easy
A student says 'I picked lottery numbers 1,2,3,4,5,6 — these can't win because they're not random.' Evaluate this claim.

Example 4

hard
Design a procedure to randomly assign 20 students into two groups of 10 for an experiment, using a random number table or calculator. Explain why randomization matters.
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