Practice Law of Large Numbers (Intuition) in Math
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
As sample size increases, the sample average approaches the true population average.
As the number of trials grows, the sample mean converges to the true expected value — randomness averages out over many trials, making the average predictable.
Example 1
easyA fair coin is flipped. Show how the proportion of heads approaches 0.5 as n increases, using simulation results: n=10: 6 heads; n=100: 53 heads; n=1000: 498 heads.
Example 2
mediumA casino game has expected value -\0.05$ per play (house edge). A player plays 10 games vs. 10,000 games. Explain how the LLN affects the likely outcome in each case.
Example 3
easyA die is rolled repeatedly and the running average is tracked. After 5 rolls, the average is 3.8. After 500 rolls, the average is 3.52. What does the LLN predict will happen to the average as rolls → ∞?
Example 4
hardA student argues: 'I've flipped heads 10 times in a row, so tails is overdue.' Using the LLN correctly, explain why this is wrong, and what LLN actually predicts.