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Statistics is the science of collecting, analyzing, and interpreting data. In any community, such as the families living in the Willbrook Farms Development, statistics helps us to understand and make sense of the information that surrounds us. Imagine you want to discover how families handle their taxes. Statistics can give us a clear picture of these behavioral patterns. For our exercise, we know that out of 20 families, 10 prepare their own taxes, 7 use a local professional, and 3 go to H&R Block. This division is called frequency distribution, which shows how data is broken down into different categories.

Understanding frequency distribution allows us to see the proportion of families in each category. It simplifies complex data, helping us to make better assessments and decisions. In our context, knowing that 50% of families handle their own taxes while the rest divide between local professionals and H&R Block is powerful statistical insight.

By using these insights from statistics, we can predict behaviors and answer specific questions, just as we did with selecting a family that prepared their own taxes.

Data analysis involves inspecting, cleansing, and modeling data to discover useful information. In our exercise, we start by retrieving the essential figures: 10 families prepared their own taxes, 7 opted for a local accountant, and 3 went to H&R Block. These numbers form the basis for our data analysis.

Data analysis helps us view the data more clearly, allowing us to answer key questions like: What is the probability of selecting a family that managed their own taxes? By interpreting data and using statistical formulas, we can dive deeper into its significance. For instance, the exercise requires calculating the probability of selecting two families who prepared their taxes independently. By analyzing the available data, we discover that this scenario's likelihood is based on conditional probability.

This type of analysis enables us to consider not only one event but also how the outcome of one affects another, leading to richer, more informative results. Probability is a strong facet of data analysis that enables conclusions in a methodical way, offering actionable insights.

Probability is the measure of how likely an event is to happen. It plays a critical role in predicting outcomes based on specific conditions. Within our exercise scenario, probability calculations let us quantify the likelihood of certain families being chosen. Let's break it down step by step.

For question a, we calculate the probability of selecting a family that prepared their taxes. This is simple:

• We have 10 families out of 20, giving us a probability of \( \frac{10}{20} = \frac{1}{2} \).

For question b, we go further to see what happens when two families are selected consecutively:

• The first family has a probability of \( \frac{1}{2} \).
• The second family reduces to \( \frac{9}{19} \) as one family is already selected.
• Thus, compounded together, the probability is \( \frac{9}{38} \).

Finally, for selecting three families, the sequence extends:

• Probability steps become \( \frac{1}{2} \times \frac{9}{19} \times \frac{4}{9} \).
• In the end, it boils down to \( \frac{1}{19} \).

This process demonstrates how each step depends on the previous outcome, called conditional probability, offering a detailed insight into complex likelihood calculations.