Question

Pet ownership Suppose that $25 \%$ of people have a dog, $29 \%$ of people have a cat, and $12 \%$ of people own both. What is the probability that someone owns a dog or a cat?

   Pet ownership Suppose that $25 \%$ of people have a dog, $29 \%$ of people have a cat, and $12 \%$ of people own both. What is the probability that someone owns a dog or a cat?

Stats Data and Models

Stats Data and Models

Richard D. De Veaux,… 4th Edition

Chapter 14, Problem 1

Instant Answer

Solved by Expert James Kiss

11/05/2022

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We are given the probabilities of owning a dog, owning a cat, and owning both. We are asked to find the probability of owning a dog or a cat. Show more…

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Pet ownership Suppose that $25 \%$ of people have a dog, $29 \%$ of people have a cat, and $12 \%$ of people own both. What is the probability that someone owns a dog or a cat?

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Key Concepts

Inclusion-Exclusion Principle

The inclusion-exclusion principle is a fundamental method used to calculate the probability of the union of overlapping events. It corrects for overcounting by adding the individual probabilities of each event and subsequently subtracting the probabilities of any intersections, ensuring that shared outcomes are only counted once.

Union of Events

The union of events in probability theory refers to the event in which at least one of several specified events occurs. It combines the individual events, acknowledging that some outcomes may satisfy more than one event simultaneously.

Probability

Probability is a measure quantifying the likelihood that a given event will occur, ranging from zero (impossibility) to one (certainty). It establishes the foundational language and rules for discussing random events and uncertainty in various contexts.

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