[T1.1] Statistical reasoning

The origins of probability theory

The notion of probability has been around for as long as people have gambled, and gambling has been around since ancient times. Everyone knows that some bets are riskier than others; betting that the next card drawn from a pack will be the queen of hearts is riskier than betting that it will be a heart. A successful gambler needs to be good at estimating the chance of winning a given bet. The notion of probability arose as a measure of chance; the higher the probability, the better the chance of winning.

Modern probability theory also arose from gambling. In the seventeenth century, mathematicians Blaise Pascal and Pierre de Fermat worked out the theory of probabilities as a response to a problem posed to Pascal by a gambler. These days, probability theory is far more than just a theory of gambling. It helps us with all kinds of risk assessment--in the insurance industry, in medical research, in engineering, and in virtually every other human endeavor.

Probability theory is the foundation of statistical reasoning, so if we are going to learn about statistical reasoning, we have to start with some probability theory. The first few sections cover the basics of probability theory, and each section ends with questions which enable you to check your understanding. The later sections contain examples of probabilistic reasoning, good and bad, including some of the most common mistakes people make when they use probabilities. If you already know how to calculate probabilities, you can skip straight to the examples.

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