Which description best captures the law of large numbers?

Which description best captures the law of large numbers?

• A. It states that events that have occurred in the past under identical conditions and resulting from unchanging causal forces will increase at a predictable rate into the future.
• B. It states that, in order to be able to predict the relative probability of future events, those events must be both frequent, and independent of one another.
• C. It states that the more times a particular event has occurred in the past, the greater the likelihood of that same event occurring in the future.
• D. It states that as the number of similar but independent exposure units increases, the relative accuracy of predictions about future outcomes also increases.

Answer: (D)

The law of large numbers says that as you collect more independent, similar trials, the observed results become more reliable and converge toward the true probability or expected value. In other words, with a big enough set of exposure units, the relative frequency of outcomes and the average outcome stabilize, making predictions about future outcomes more accurate. That’s why the best description is the one that notes increasing the number of independent, similar trials makes predictions more accurate. For example, flipping a fair coin many times will yield a proportion of heads that gets closer to 0.5 as the number of flips grows, and counting claims across a large portfolio of policies gives a more precise estimate of the expected claim rate. Other statements are less accurate because they either imply determinism from past events, require conditions beyond independence and large sample size, or suggest that past occurrences inherently raise the likelihood of future ones despite independence.

The law of large numbers says that as you collect more independent, similar trials, the observed results become more reliable and converge toward the true probability or expected value. In other words, with a big enough set of exposure units, the relative frequency of outcomes and the average outcome stabilize, making predictions about future outcomes more accurate.

That’s why the best description is the one that notes increasing the number of independent, similar trials makes predictions more accurate. For example, flipping a fair coin many times will yield a proportion of heads that gets closer to 0.5 as the number of flips grows, and counting claims across a large portfolio of policies gives a more precise estimate of the expected claim rate.

Other statements are less accurate because they either imply determinism from past events, require conditions beyond independence and large sample size, or suggest that past occurrences inherently raise the likelihood of future ones despite independence.