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Understanding the statistics regarding internet access is crucial for a variety of social and economic analyses. The 2013 Pew poll reflects a significant milestone in connectivity, stating that 93% of young adults in the United States have internet access. These statistics aren't just numbers; they provide insights into the digital divide, educational opportunities, and the spread of information.

Beyond the raw data, analyzing access trends requires consideration of demographic factors, such as age, location, and household composition, which can influence the probability of individuals having internet access. It's important to note that statistics may vary over time due to changes in technology, policies, or social behaviors. In probabilistic terms, these statistics help us to establish base rates, which are the foundational probabilities used for further calculations.

Calculating probabilities is one of the foundational techniques in statistics, allowing us to assess the likelihood of various outcomes. To perform these calculations, especially with independent events, the multiplication rule is often used. For instance, if the probability of one event happening is 0.93 (or 93%), and the event is independent of another of the same likelihood, the combined probability is the product of the two single probabilities.

In the case of our exercise, the individual probability that a young adult has internet access is 0.93, and the combined probability that two independent randomly selected young adults have internet access would be calculated as:\[\begin{equation}0.93 \times 0.93 = 0.8649\end{equation}\]This result of 0.8649, or 86.49%, represents how likely both events are to occur together, considering they are independent. Understanding how to apply the multiplication rule is essential for accurately determining the likelihood of compound events.

Independence is a key concept in probability that refers to the quality of two or more events not affecting each other's outcomes. For two events to be independent, the occurrence of one must not change the probability of the occurrence of the other. This assumption is critical for certain probability calculations.

In our discussed exercise, while two randomly selected individuals might independently have internet access, a married couple in the same household does not exhibit the same independence. Their access is not independent because it is affected by common factors, such as financial decisions or service availability within their shared residence. It's essential to distinguish dependent from independent events, as it significantly affects the approach to probability calculations and the accuracy of our predictions.