Question

In a study of bird migration, a researcher recorded on a certain day a total of 262 birds, consisting of 65 geese, 84 ducks, and 113 robins in the skies. Below, show a possible equation for calculating the probability that a random bird chosen from among these is NOT a duck. (For this practice test, write the numbers in the boxes below.) 65 84 113 262

Short answer

The probability that a random bird chosen from among these is not a duck is \(\frac{89}{131}\).

Step-by-step solution

Determine the number of birds that are not ducks

Since there are 65 geese, 84 ducks, and 113 robins, we can calculate the total number of birds that are not ducks by adding the number of geese and robins: Number of non-duck birds = Number of geese + Number of robins

Calculate the probability

To find the probability that a random bird chosen from among these is not a duck, we divide the number of non-duck birds (from Step 1) by the total number of birds (which is 262): Probability (not a duck) = \(\frac{\text{Number of non-duck birds}}{\text{Total number of birds}}\) Now, let's complete these calculations.

Calculate the number of non-duck birds

Using the numbers given in the problem, we calculate the number of non-duck birds as follows: Number of non-duck birds = 65 geese + 113 robins = 178

Calculate the probability

Now, let's plug in the numbers we calculated into the formula from Step 2: Probability (not a duck) = \(\frac{178}{262}\) Simplify the fraction to get the final probability: Probability (not a duck) = \(\frac{89}{131}\) So, the probability that a random bird chosen from among these is not a duck is \(\frac{89}{131}\).

Key concepts

Bird Migration Study

The fascinating natural phenomenon of bird migration offers an excellent context to explore the use of probability in real-world scenarios. Researchers often observe various species, such as geese, ducks, and robins, to understand patterns in migration. When studying bird migration, scientists can use probability to make predictions or analyze trends in the data collected.

For instance, in the given exercise, a researcher monitoring the skies documented different species and their respective quantities. This data can then be used to calculate the likelihood of randomly spotting a certain species, which is not only interesting from a research standpoint but also demonstrates probabilistic reasoning in action. The exercise also subtly reinforces an important concept in probability: the complement rule, where the probability of an event not occurring is simply one minus the probability of the event occurring.

Probability Theory

Probability theory is a branch of mathematics concerned with quantifying random events. The core concept here is that probability is the measure of how likely an event is to occur. Mathematically, it is expressed as a number between 0 and 1, where 0 indicates impossibility, and 1 signifies certainty. Commonly, it's represented as a fraction, percentage, or decimal.

In real-world terms, probability can predict anything from weather forecasts to the likelihood of a non-duck bird being chosen at random, as seen in our example. Understanding basic probability calculations is essential, as it not only helps in interpreting data but also strengthens the foundation for more complex statistical concepts.

GED Mathematics Prep

The General Educational Development (GED) tests are a suite of four subject tests which, when passed, certify that the test taker has American or Canadian high school-level academic skills. Mathematics is a critical component of the GED, and understanding probability is an aspect of the math curriculum.

Exercises like our bird migration study problem are typical of the questions that may appear in a GED exam, testing skills in reasoning and mathematical logic. Emphasizing probability in GED mathematics prep enables students to tackle a wide variety of questions, reinforcing critical thinking and problem-solving skills. It demonstrates not only the ability to perform computations but also to understand and apply mathematical concepts in various contexts.

Probabilistic Reasoning

Probabilistic reasoning refers to the process of making assertions or predictions based on the likelihood of various outcomes. It's a way of thinking that evaluates the occurrence of events in terms of probabilities rather than certainties. This form of reasoning is essential for informed decision-making and is utilized in fields like statistics, artificial intelligence, economics, and risk assessment.

In the context of our bird migration example, probabilistic reasoning aids in deducing that a bird picked at random is less likely to be a duck by examining the proportion of ducks relative to other birds. This method of reasoning is not only foundational for students learning probability but is also a valuable critical thinking skill, helping to navigate everyday decisions and understand world phenomena through the lens of probability.