Law of large numbers
Probability theory · Mathematics
Study notes
Q: A die is rolled many times. After 6000 rolls, about what average is expected? μ = 3.5. By the law of large numbers, X̄₆₀₀₀ ≈ 3.5 (very close). After only 6 rolls the average could be far off; after 6000 it hugs 3.5. Casinos rely on this: the house edge emerges over thousands of bets!