Question

The land area of the state of Alaska is $571,951$ square miles. The land area of the United States is $3,537,438$ square miles. If a point is chosen at random in the United States, what is the probability that it is in Alaska?

Name: Problem 17, Chapter 11: Geometry
Uploaded: 2020-07-06T23:59:30-08:00
Duration: 1 min 37 s
Channel: Alaina Shelton
Description: The land area of the state of Alaska is 571,951 square miles. The land area of the United States is 3,537,438 square miles. If a point is chosen at random in the United States, what is the probability that it is in Alaska?

   The land area of the state of Alaska is $571,951$ square miles. The land area of the United States is $3,537,438$ square miles. If a point is chosen at random in the United States, what is the probability that it is in Alaska?

Geometry

Cindy J. Boyd, Jerry… 1st Edition

Chapter 11, Problem 17

Instant Answer

Solved by Expert Alaina Shelton

07/06/2020

Step 1

We are given the land area of Alaska and the total land area of the United States. We are asked to find the probability that a point chosen at random in the United States is in Alaska. Show more…

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The land area of the state of Alaska is $571,951$ square miles. The land area of the United States is $3,537,438$ square miles. If a point is chosen at random in the United States, what is the probability that it is in Alaska?

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Key Concepts

Uniform Random Distribution

A uniform random distribution assumes that every point within a given region has an equal likelihood of being selected. This concept is crucial when determining probabilities based on areas, as it justifies using the ratio of a specific area to a total area.

Classical Probability

Classical probability is a fundamental concept where the probability of an event is defined as the ratio of the number of favorable outcomes to the total number of outcomes. This allows us to compute probabilities in a broad range of problems where outcomes are equally likely.

Area Ratios in Probability

When dealing with geometric or spatial probability problems, the probability is calculated by taking the ratio of the favorable area (the area of interest) to the total area under consideration. This approach translates spatial dimensions into probabilities by comparing parts of a whole.

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