Question

Suppose that $20 \%$ of all adults in a small town live alone, and $8 \%$ of the adults live alone and have at least one pet. What is the probability that a randomly selected adult from this town has at least one pet given that this adult lives alone?

Name: Problem 99, Chapter 4: Introductory Statistics
Uploaded: 2022-04-08T18:33:56-08:00
Duration: 48 s
Channel: Nick Johnson
Description: Suppose that 20 % of all adults in a small town live alone, and 8 % of the adults live alone and have at least one pet. What is the probability that a randomly selected adult from this town has at least one pet given that this adult lives alone?

   Suppose that $20 \%$ of all adults in a small town live alone, and $8 \%$ of the adults live alone and have at least one pet. What is the probability that a randomly selected adult from this town has at least one pet given that this adult lives alone?

Introductory Statistics

Prem S. Mann 7th Edition

Chapter 4, Problem 99

Instant Answer

Solved by Expert Nick Johnson

04/08/2022

Step 1

We are given that the probability of A, P(A), is 0.2 and the probability of both A and P, P(A ∩ P), is 0.08. Show more…

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Suppose that $20 \%$ of all adults in a small town live alone, and $8 \%$ of the adults live alone and have at least one pet. What is the probability that a randomly selected adult from this town has at least one pet given that this adult lives alone?

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Key Concepts

Joint Probability

Joint probability refers to the probability of two events occurring simultaneously. It is crucial for determining conditional probabilities, as it represents the numerator P(A ? B) in the formula, indicating how frequently both scenarios happen together.

Probability Ratio

The probability ratio involves dividing the joint probability of two events by the probability of one of the events. This operation converts the joint probability into a conditional probability, effectively recalculating the likelihood of one event under the condition that the other has occurred.

Conditional Probability

Conditional probability is a measure of the probability of an event occurring given that another event has already occurred. It is expressed by the formula P(A|B) = P(A ? B) / P(B), which provides a framework for updating the likelihood of events based on new information.

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