1. Probability: Making Sense of Uncertainty

Individual outcomes can be surprising, but repeated trials often settle into stable patterns. This idea explains why casinos, polls, quality checks, and scientific studies can make useful predictions from randomness.

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The chance of an event can change when we receive new information. Conditional probability helps explain medical screening results, weather forecasts, spam filters, and why two linked events should not be treated as independent.

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Probability supports decisions by weighing possible outcomes against their chances and consequences. Expected value appears in insurance, product planning, games, experiments, and choices where no result is guaranteed.

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People use probability to model floods, test medicines, price insurance, analyze elections, build machine-learning systems, and study nature. Small projects—such as simulating a queue or testing a prediction—can turn uncertain situations into evidence.

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Review this chapter with practice based on your mistakes.