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5.1,5.2) WW Score: \( 10 \%, 5 \) of 50 points Select the correct choice that completes the sentence below. A represents scenarios where the outcome of any particular trial of an experiment is unknown, but the proportion (or relative frequency) a particular outcome is observed approaches a specific value.

Ask by Hammond Marshall. in the United States
Mar 19,2025

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\(A\) represents repeated random experiments where, although any particular outcome is uncertain, the long-run relative frequency converges to a specific value.

Solución

1. We are given scenarios in which the outcome of any single trial of an experiment is unknown, yet when we repeat the experiment many times, the relative frequency of a particular outcome converges to a specific value. 2. This description is the basis for the frequentist interpretation of probability. In this view, although any individual outcome is uncertain, if the experiment is repeated independently a large number of times, the proportion of times that a given outcome occurs tends to stabilize at a fixed number. 3. This phenomenon is formalized by the law of large numbers, which guarantees that, as the number of trials increases, the sample relative frequency approaches the true probability of the event. 4. Hence, the missing word in the sentence is referring to repeated random experiments (or trials) that exhibit this property. 5. The correct completion of the sentence is that \(A\) represents repeated random experiments with outcomes determined by chance. Final Answer: \(A\) represents repeated random experiments where, although any particular outcome is uncertain, the long-run relative frequency converges to a specific value (i.e., the probability).

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Bonus Knowledge

This concept is key in probability theory and statistics, especially when discussing the law of large numbers. It's like tossing a coin: while you can’t predict the outcome of a single toss, over many tosses, the proportion of heads will get closer and closer to 50%. This principle is what allows statisticians to make predictions based on sample data! In real-world scenarios, this principle is used in fields like quality control and insurance to assess risk. For instance, manufacturers use it to determine how often defects occur in production runs, predicting that over time, the proportion of defective items will stabilize. So, whether you're flipping a coin or analyzing data, the exciting world of probability dynamics offers thrilling insights!

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