Calculating Probability Gerbils And Snakes In A Pet Shop

In this article, we will delve into a fascinating probability problem involving animals in a pet shop. Specifically, we'll explore the scenario where 2/13 of the animals are gerbils and 5/13 are snakes, and we aim to determine the probability of randomly selecting either a gerbil or a snake. This is a classic example of calculating probabilities of mutually exclusive events, a fundamental concept in mathematics. Understanding these concepts is crucial not only for academic purposes but also for real-world applications, such as risk assessment, statistical analysis, and even everyday decision-making. By the end of this article, you will gain a clear understanding of how to calculate probabilities in similar situations, empowering you to tackle a variety of problems with confidence. Let's embark on this journey of probability and explore the intriguing world of gerbils and snakes in a pet shop.

Problem Statement: Probability in Pet Shop Animals

Probability is a fundamental concept in mathematics that quantifies the likelihood of an event occurring. Understanding probability is crucial in various real-world applications, from statistical analysis to risk assessment. In this particular scenario, we are presented with a pet shop where a fraction of the animals are gerbils and another fraction are snakes. Our goal is to determine the probability that an animal chosen at random from the pet shop will be either a gerbil or a snake. This problem exemplifies the concept of mutually exclusive events, where the occurrence of one event (choosing a gerbil) precludes the occurrence of the other event (choosing a snake). To solve this, we need to understand how to combine probabilities of such events. The problem sets the stage for exploring basic probability calculations and understanding how fractions can represent probabilities in a practical context. Let’s dive deeper into the specifics of the problem and break down the steps needed to arrive at the solution.

Given that 2/13 of the animals in a pet shop are gerbils and 5/13 are snakes, what is the probability that an animal chosen at random is a gerbil or a snake? Give your answer as a fraction. This question is a practical application of probability in a straightforward scenario. It requires us to understand how to combine probabilities of mutually exclusive events, meaning events that cannot occur simultaneously. In this case, an animal cannot be both a gerbil and a snake at the same time. Therefore, the probability of choosing a gerbil or a snake is the sum of the individual probabilities of choosing a gerbil and choosing a snake. This problem is not just an exercise in mathematics; it mirrors real-world situations where understanding probability can aid in decision-making, from assessing risks to making predictions. To solve this, we will add the fractions representing the probabilities of each event, ensuring we adhere to the rules of fraction addition. The final answer will be a fraction, representing the likelihood of selecting either a gerbil or a snake from the pet shop.

Breaking Down the Probability Problem

To effectively tackle this probability problem, we need to break it down into manageable steps. The initial step involves identifying the individual probabilities of each event. We are given that 2/13 of the animals are gerbils and 5/13 are snakes. These fractions directly represent the probabilities of choosing a gerbil and choosing a snake, respectively. It is crucial to recognize that these two events are mutually exclusive, meaning they cannot happen at the same time – an animal cannot be both a gerbil and a snake. This understanding is key because it allows us to use the addition rule for mutually exclusive events. The next step is to apply this rule, which states that the probability of either one of two mutually exclusive events occurring is the sum of their individual probabilities. In mathematical terms, if P(A) is the probability of event A and P(B) is the probability of event B, then the probability of either A or B occurring is P(A) + P(B). By understanding this rule and applying it to our specific problem, we can determine the overall probability of choosing a gerbil or a snake. This methodical approach simplifies the problem and ensures we arrive at the correct solution.

Solving for the Probability of Selecting a Gerbil or a Snake

To solve this probability problem, we start by acknowledging the given information: 2/13 of the animals are gerbils and 5/13 are snakes. These fractions represent the probabilities of randomly selecting a gerbil and a snake, respectively. Since these events are mutually exclusive, meaning that an animal cannot be both a gerbil and a snake, we can use the rule of addition for mutually exclusive events. This rule states that the probability of either event A or event B occurring is the sum of their individual probabilities, which is expressed as P(A or B) = P(A) + P(B). In our case, event A is selecting a gerbil, and event B is selecting a snake. Therefore, we need to add the probabilities of these two events. The probability of selecting a gerbil is 2/13, and the probability of selecting a snake is 5/13. To find the probability of selecting either a gerbil or a snake, we add these two fractions: 2/13 + 5/13. Since the denominators are the same, we simply add the numerators: (2 + 5) / 13 = 7/13. This result, 7/13, represents the probability that an animal chosen at random from the pet shop will be either a gerbil or a snake. It's a straightforward application of basic probability principles and fraction addition.

Detailed Solution: Adding Fractions for Probability

The heart of solving this probability question lies in the addition of fractions. We know that the probability of selecting a gerbil is 2/13, and the probability of selecting a snake is 5/13. To find the combined probability of selecting either a gerbil or a snake, we must add these two fractions together. The fundamental rule for adding fractions states that if the fractions have the same denominator, you can simply add the numerators and keep the denominator the same. In our case, both fractions, 2/13 and 5/13, have the same denominator, which is 13. This simplifies our task significantly. We add the numerators, 2 and 5, which gives us 7. The denominator remains 13. Thus, the sum of the fractions is 7/13. This fraction, 7/13, is the probability of selecting either a gerbil or a snake from the pet shop. It represents that out of 13 animals, 7 are either gerbils or snakes. Understanding this process of fraction addition is not only crucial for solving this particular problem but also for many other mathematical and real-world scenarios involving probabilities and proportions. The simplicity of this calculation underscores the elegance of basic arithmetic principles in solving practical problems.

The Answer: Probability as a Fraction

After meticulously calculating the probabilities, we arrive at the solution for this problem. The probability that an animal chosen at random from the pet shop is either a gerbil or a snake is 7/13. This fraction represents the likelihood of selecting either a gerbil or a snake out of the total number of animals considered. The numerator, 7, signifies the combined number of gerbils and snakes, while the denominator, 13, represents the total number of animals used as the basis for the fractions given in the problem. This answer is presented as a fraction, as requested in the problem statement, providing a clear and concise representation of the probability. The fraction 7/13 indicates that if you were to randomly select an animal from the pet shop, there are 7 chances out of 13 that you would pick either a gerbil or a snake. This result is a direct application of probability theory, specifically the addition rule for mutually exclusive events, and it demonstrates how fractions can effectively quantify likelihoods in real-world scenarios. The solution not only answers the question but also reinforces the understanding of probability calculations and their practical implications.

Conclusion: Applying Probability Concepts

In conclusion, we have successfully determined the probability of selecting either a gerbil or a snake from a pet shop, given that 2/13 of the animals are gerbils and 5/13 are snakes. By applying the fundamental principles of probability, specifically the addition rule for mutually exclusive events, we calculated the combined probability to be 7/13. This means that there is a 7 out of 13 chance that a randomly chosen animal will be either a gerbil or a snake. This problem serves as an excellent example of how probability concepts can be applied to everyday situations. The ability to calculate probabilities is a valuable skill, not only in mathematics but also in various fields such as statistics, finance, and even decision-making in daily life. Understanding how to combine probabilities of mutually exclusive events allows us to make informed predictions and assessments. The solution to this problem highlights the importance of breaking down complex scenarios into simpler components and applying the appropriate mathematical rules. By mastering these basic concepts, one can confidently tackle more intricate probability problems and gain a deeper appreciation for the role of probability in the world around us.