Practice Randomness in Math

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

Quick Recap

The quality of having no predictable pattern; outcomes are uncertain but follow probability rules.

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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