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The law of large numbers states that for independent repeated trials with a common success probability $p$, the observed success proportion approaches $p$ as the number of trials grows. This is a long-run tendency specified by the law, meaning that while individual short-term outcomes may vary, the cumulative average stabilizes around the theoretical value over many repetitions.

Conditions: The trials are independent.; Each trial shares a common success probability $p$.; The number of trials grows large.

The law of large numbers states that for independent repeated trials with a common success probability $p$, the observed success proportion approaches $p$ as the number of trials grows. This is a long-run tendency specified by the law, meaning that while individual short-term outcomes may vary, the cumulative average stabilizes around the theoretical value over many repetitions.

Conditions: The trials are independent.; Each trial shares a common success probability $p$.; The number of trials grows large.