Probability Of A Defect-Free Mouse: A Step-by-Step Guide

by SLV Team 57 views

Hey guys! Let's dive into a probability problem. Suppose we have a store selling computer mice, and we know that out of every 125 mice, 12 of them have some kind of defect. Our mission, should we choose to accept it, is to figure out the probability that a randomly selected mouse doesn't have a defect. Sounds like fun, right?

Understanding the Problem: The Basics of Probability

First things first, let's break down what probability even is. Probability, in a nutshell, is a way of measuring how likely something is to happen. It's expressed as a number between 0 and 1, or as a percentage between 0% and 100%. A probability of 0 means the event is impossible (like a cat giving birth to a toaster – not gonna happen!). A probability of 1 (or 100%) means the event is a sure thing (like the sun rising tomorrow – fingers crossed!).

In our case, we're dealing with the probability of a mouse being defect-free. This means we need to figure out the ratio of defect-free mice to the total number of mice. Think of it like this: if you flip a coin, the probability of getting heads is 1/2 (or 50%) because there's one favorable outcome (heads) out of two possible outcomes (heads or tails). We'll apply this same logic to our mice problem.

Now, let's get into the specifics of the problem. We know there are 125 mice total, and 12 of them are defective. That means the rest aren't defective. This is the key piece of information we need to solve the problem. Remember, we are trying to find the probability of randomly choosing a mouse that is not defective. This requires a few simple calculations, so let's get started. We'll outline each step to help you follow along.

Calculating the Number of Defect-Free Mice

This is the easy part, folks! We know the total number of mice (125) and the number of defective mice (12). To find the number of defect-free mice, we simply subtract the number of defective mice from the total number of mice. So, we have the following calculation:

Defect-free mice = Total mice - Defective mice Defect-free mice = 125 - 12 Defect-free mice = 113

So, there are 113 defect-free mice. That's a good start! We're making progress. We're now one step closer to solving our probability problem. We have calculated the number of defect-free mice. Remember that this number is an essential component to solve our probability question. Now, with this information, we will calculate the probability of the event. Onward!

Calculating the Probability

Now that we know how many defect-free mice we have, we can calculate the probability of randomly selecting one. The probability is calculated as follows:

Probability = (Number of favorable outcomes) / (Total number of possible outcomes)

In our case:

  • Favorable outcome: Selecting a defect-free mouse (and we know there are 113 of these).
  • Total possible outcomes: Selecting any mouse from the store (and we know there are 125 mice in total).

So, the probability is:

Probability = 113 / 125

Let's do the math. When you divide 113 by 125, you get 0.904. To express this as a percentage, we multiply by 100: 0.904 * 100 = 90.4%. This is a high probability, which makes sense since there are far more non-defective mice than defective ones. This result should provide confidence that we are on the right track!

The Answer: Probability of a Defect-Free Mouse

Therefore, the probability of selecting a defect-free mouse is 0.904, or 90.4%. This means that if you randomly pick a mouse from the store, there's a very good chance it won't have any defects. Awesome, right? Congratulations, we solved the problem! Feel proud of yourself. This is an awesome accomplishment. The steps outlined here provide a solid foundation for approaching similar probability problems.

Key Takeaways and Tips for Solving Probability Problems

Here are some key takeaways from this problem and some general tips for tackling probability questions:

  • Identify the favorable outcome: What are you trying to find the probability of? In our case, it was a defect-free mouse.
  • Identify the total possible outcomes: What is the total number of possibilities? Here, it was the total number of mice.
  • Use the formula: Probability = (Favorable outcomes) / (Total outcomes). Always use this formula!
  • Convert to percentage (optional): To make the probability easier to understand, convert it to a percentage by multiplying by 100.
  • Break down the problem: If the problem seems complex, break it down into smaller, more manageable steps. This will make it easier to solve. Like we did with calculating the number of defect-free mice.
  • Double-check your work: Make sure your answer makes sense in the context of the problem. A probability should always be between 0 and 1 (or 0% and 100%).
  • Practice: The more you practice probability problems, the easier they'll become. Seriously. Do more problems to learn even better.

Probability in the Real World

Probability isn't just a math problem, guys; it's everywhere! Here are some examples:

  • Weather forecasting: Meteorologists use probability to predict the chance of rain, snow, or sunshine.
  • Insurance: Insurance companies use probability to assess the risk of events, like car accidents or house fires, and set premiums accordingly.
  • Gambling: Casinos and lotteries are all about probability (though the odds are usually stacked against you!).
  • Medical diagnoses: Doctors use probability to assess the likelihood of a patient having a certain disease based on symptoms and test results.
  • Everyday decision-making: Even in everyday decisions, such as deciding what route to take to work (considering traffic), we are implicitly using probability to weigh the potential outcomes.

Conclusion: You Got This!

So there you have it! We've successfully calculated the probability of selecting a defect-free computer mouse. Probability problems can seem tricky at first, but with a little practice and the right approach, you can master them. Remember the steps, practice regularly, and don't be afraid to ask for help if you need it. Keep in mind that math can be fun! Also, remember to think about the bigger picture and how probability relates to the world around you. You are now equipped with the knowledge and skills to tackle similar problems. Keep up the great work. Now go forth and conquer those probability problems!