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Statistics is the science that helps us make sense of data. It involves collecting, analyzing, interpreting, and presenting data. In our example, statistics help us understand the dietary habits of 275 students. - We identified 20 students who are vegetarians. This is part of data collection; gathering specific information from the larger group.
- With statistics, we can not only count the vegetarians, but also analyze further, like figuring out who eats fish or eggs. This analysis gives deeper insight into our sample. Understanding statistics lets us see the bigger picture and make informed predictions or decisions based on numerical data.

In probability, the sample space is the set of all possible outcomes of an experiment or scenario. It provides a complete list of everything that can happen in a situation, helping to calculate the likelihood of each outcome. - For our exercise, the sample space involves the dietary choices of the 20 vegetarian students.
- Every student’s choice, whether they eat fish, eggs, both, or neither, represents a different outcome in our sample space. By clearly defining the sample space, we ensure that we account for every possible scenario, making our probability analysis accurate and comprehensive.

Probability calculation is about finding the likelihood that a particular event will happen. This is done by dividing the number of successful outcomes by the total number of outcomes.- In our problem, to find out how many vegetarians eat neither fish nor eggs, we use the formula: \[ \text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \] - Here, the probability that a student eats neither is calculated as \( \frac{8}{20} \), where 8 is the number of vegetarians who eat neither fish nor eggs, and 20 is the total number of vegetarians.After simplifying the fraction to \( \frac{2}{5} \), we find the probability to be 0.4, or 40% chance, that a randomly selected vegetarian eats neither fish nor eggs.

Event outcomes refer to the potential results or outputs from a chance experiment. Each outcome shows how the events can occur. - In our scenario, each vegetarian's dietary choice is an outcome. This includes whether they eat fish, eggs, both, or neither.
- Understanding these outcomes helps us determine probabilities. Each outcome shows a different possibility that can happen when we pick a vegetarian at random. Determining and listing event outcomes ensures we don't miss any possibilities, which is crucial for accurate probability calculations. In this way, we can precisely determine the chance of each dietary choice.