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Lesson Overview
Section* *

Figure 7.1 illustrates key aspects of the Statistical Paradigm. We are interested in the characteristics of a **population** or how it might behave under different real-world conditions. To investigate, we take an appropriate **sample** or compare samples under different conditions (Lessons 1 and Lesson 2). Our samples then produce data that must be described and/or compared using appropriate measures, **statistical summaries, and pictures **(Lesson 3 to Lesson 6). Next, in order to use those statistics to make **inferences** about the **population**, we must consider what types of samples or differences between groups might happen just by chance - that is the topic of **probability** that we examine in this lesson.

Life is riddled with decisions that must be made in the face of uncertainty. What time should your friend pick you up at the airport given the uncertainty in the arrival time of your flight? Should you take an umbrella on your hike given the uncertainty in the weather forecast? Is it better to have the surgery or take the new medication given the uncertainty in the clinical outcome? Should you bet on the favorites or go for the underdogs in your office March Madness basketball pool? Statistics help us to address the myriad of problems of this type by directly quantifying the uncertainties in life. Probability is the language of certainty. This lesson provides insights into this language's basic grammar - the rules that govern the quantification of uncertainty.

## Objectives

- Identify and apply the relative frequency interpretation of probability.
- Apply the basic rules of probability.
- Set up a calculation for and interpret an expected value.
- Interpret how proportions and averages converge when the chance process generating them is repeated independently.
- Set up and interpret a random simulation to estimate a probability.