Chapter 2. Probability

Probability theory is fundamental to statistics. Some people find probability to be an intimidating topic, but there’s no reason anyone willing to put in the time can’t come to understand it at the level necessary to succeed in statistics. As is the case in many fields of study, advanced probability theory can become very complex and difficult to understand, but the basic principles of probability are intuitive and easy to comprehend. What’s more, most people are already familiar with probabilistic statements, from the weather report that tells you there is a 30% chance of rain this afternoon to the warning on cigarette packages that smoking increases your risk of developing lung cancer.

If, like most adults, you hold one or more insurance policies, you are already engaged in an enterprise based on probabilistic reasoning. If you drive or own an automobile, for instance, you probably have an automobile insurance policy, which should really be called an automobile expenses insurance policy because it protects the policyholder against the extreme expenses that can be incurred due to an accident. People don’t purchase insurance policies because they are planning to get into a crash; rather, they acknowledge that there is a nonzero probability of such an event occurring in the future.

Governments often require automobile owners to have insurance policies for the same reason; this requirement is not a judgment that you are a bad driver, just an acknowledgment that ...

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