Randomness Math Example 1
Follow the full solution, then compare it with the other examples linked below.
Example 1
easyA 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.
Solution
- 1 Each coin flip is an independent random event with
- 2 The coin has no memory — past outcomes do not affect future ones
- 3 Probability of tails on flip 11: still exactly , regardless of previous 10 heads
- 4 The Gambler's Fallacy: incorrectly believing that past random events influence future independent ones
Answer
. Past flips do not affect future independent flips.
Randomness means each trial is independent of all previous trials. The Gambler's Fallacy is one of the most common probability misconceptions. True randomness has no 'memory' — each trial starts fresh regardless of history.
About Randomness
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.
Learn more about Randomness →More Randomness Examples
Example 2 medium
A random number generator produces: 3, 7, 1, 9, 2, 8, 5, 4, 6, 10 (each number 1-10 equally likely).
Example 3 easyA student says 'I picked lottery numbers 1,2,3,4,5,6 — these can't win because they're not random.'
Example 4 hardDesign a procedure to randomly assign 20 students into two groups of 10 for an experiment, using a r