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.Land in Canada. Canada's national statist ics agency, Statistics Canada, says that the land area of Canada is \(9,094,000\) square kilometers. Of this land, 4,176, 000 square kilometers are forested. Choose a square kilometer of land in Canada at random. (Assume a selected square is classified as either forested or not forested.) a. What is the probability that the area you chose is forested? b. What is the probability that it is not forested?

Short Answer

Expert verified
a. 0.4594; b. 0.5406

Step by step solution

01

Understand the Total Land Area

The total land area of Canada is given as 9,094,000 square kilometers. This is the denominator we will use for calculating probabilities.
02

Identify Forested Land Area

The forested land area is 4,176,000 square kilometers. This is the numerator for calculating the probability of selecting a forested square kilometer.
03

Calculate Probability of Choosing Forested Land

The probability that a chosen square kilometer is forested is calculated by dividing the forested land by the total land: \[ P( ext{forested}) = \frac{4,176,000}{9,094,000} \approx 0.4594 \]
04

Calculate Probability of Choosing Non-Forested Land

First, find the non-forested land by subtracting the forested land from the total land: \[ 9,094,000 - 4,176,000 = 4,918,000 \] Then, calculate the probability of non-forested land: \[ P( ext{not forested}) = \frac{4,918,000}{9,094,000} \approx 0.5406 \]
05

Verify Probability Completeness

The sum of both probabilities should equal 1 because all land is either forested or not forested. \[ P( ext{forested}) + P( ext{not forested}) = 0.4594 + 0.5406 = 1 \]

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Statistics
Statistics is a fascinating field that deals with collecting, analyzing, interpreting, and presenting data. In the context of the exercise, it helps in determining the likelihood of an event, such as picking a forested area in Canada. Probability, a key branch of statistics, measures how likely an event is to happen.
To calculate probability, we divide the favorable outcomes by the total number of possible outcomes. In our example, the total land area of Canada is the complete set of possible outcomes, while the forested area represents the favorable outcomes.
  • Statistics and probability are fundamental for data-driven decision making.
  • They help to understand trends and patterns in large datasets.
  • Probabilities are often expressed as percentages or decimals.
Understanding statistics and probability is crucial, as they help us to forecast different scenarios and make informed decisions in various fields, including environmental science, economics, and everyday life.
Forest Area Calculation
Calculating forest area involves finding the section of land covered with trees and shrubbery. For the exercise, this was critical in determining the probability of selecting a piece of forested land.
By using the given data, we calculated the percentage of land that is forested. We discovered that the forested land area in Canada is approximately 45.94% of the total.
Here's how the calculation works:
  • Identify the total land area: 9,094,000 square kilometers.
  • Identify the forested land area: 4,176,000 square kilometers.
  • Calculate the probability: Divide the forested land area by the total land area. In mathematical terms, this is expressed as \[ P(\text{forested}) = \frac{4,176,000}{9,094,000} \approx 0.4594 \].
By calculating these probabilities, we can better understand the extent to which Canada is forested, offering insights into its natural environment and contributing to environmental policy planning.
Land Area Analysis
Land area analysis involves examining the proportions or percentages of different types of land. This helps in understanding the geographical and environmental layout of a region.
In our context, this meant analyzing forested versus non-forested land in Canada. Knowing that 54.06% of Canada's land is not forested helps in planning for land use, conservation efforts, and urban development.
Here's the analysis breakdown:
  • Total land area: 9,094,000 square kilometers.
  • Forested land: 4,176,000 square kilometers (previously calculated as 45.94%).
  • Non-forested land: 4,918,000 square kilometers. Calculate as \[ P(\text{not \ forested}) = \frac{4,918,000}{9,094,000} \approx 0.5406 \].
Performing a land area analysis helps in identifying available resources for various uses, ensuring sustainable development, and preserving environmental quality.

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