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# Probability

If four people drop their identical cell phones in a crowded elevator and then pick them up at random, how likely is it that at least one person will pick up the right phone? How many people will pick up the correct phone on average in the long run? In this topic, you will analyze this scenario to learn the basic ideas of probability. Other questions this topic addresses include: How likely is it that a family with two children will have one boy and one girl? What about a family with four children? Are they more likely to have two children of each sex or a 3:1 gender breakdown? The study of probability will help you answer such questions, and you may even find yourself surprised by some of the answers. Applying probability methods to statistical issues will also help you answer questions such as how likely is it that random assignment will produce an equal split of genders between two treatment groups.

## Overview

In the previous two units, you studied methods for analyzing data, from displaying them graphically to describing them verbally and numerically. In Topics 4 and 5, you learned how to collect data by taking a random sample from a population or by randomly assigning subjects to treatment groups. At first glance, you might think that introducing randomness into the process would make it more difficult to draw reliable conclusions. Instead, you will find that randomness actually produces predictable, longrun patterns that allow you to quantify how closely ...

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