The 820 Children At A Certain School Were Asked What They Pr

The 820 Children At A Certain School Were Asked What They Prefer To Dr

The school collected data from 820 children regarding their preferred beverage to drink with lunch. The responses included the following categories: soft drinks (341 children), milk/chocolate milk (210 children), water (97 children), tea (38 children), and other (134 children). Despite the variety in responses, the school only serves milk, chocolate milk, or water with lunch. The goal is to determine the probability that the first student in line for lunch will be served their preferred beverage given the available options.

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Determining the probability that the first student in line will be served their preferred beverage involves analyzing the provided data and understanding the context of available lunch options. Since the school only serves three types of beverages—milk, chocolate milk, and water—we need to ascertain the likelihood that the student's preferred drink aligns with the offerings. This process entails calculating the proportion of students whose preferences match the served beverages and then translating that into the probability for a randomly selected student.

Given the total number of students surveyed is 820, the distribution of preferences is as follows:

  • Soft drinks: 341 students
  • Milk/chocolate milk: 210 students
  • Water: 97 students
  • Tea: 38 students
  • Other: 134 students

Since the school serves only milk, chocolate milk, or water, the preferences that can be directly matched with available options are categorized under milk/chocolate milk and water. Preferences for soft drinks, tea, or other are not covered by the lunch offerings.

To find the probability that the first student is served their preferred beverage, we focus on the likelihood that their preference matches one of the available options. Assuming the students' preferences are randomly distributed, and that the serving options are equally available to all, the probability is based on the proportion of students who prefer exactly what's served.

Calculating the total number of students whose preferences align with the available beverages: the sum of students preferring milk/chocolate milk and water, that is, 210 + 97 = 307 students. The remaining students prefer drinks not available with lunch (soft drinks, tea, and other), totaling 341 + 38 + 134 = 513 students.

The probability that a randomly selected student prefers a beverage that the school serves is the ratio of students who prefer such beverages to the total number of students surveyed:

Probability = (Number of students preferring served beverages) / (Total students)


= 307 / 820


≈ 0.3744

Rounding this probability to two decimal places gives approximately 0.37. Therefore, there is a 37% chance that the first student in line will be served their preferred beverage with their lunch, assuming randomness and equal likelihood of preferences across the student body.

It is important to note that this model assumes uniform preference distribution and does not account for individual ordering preferences or possible variations in beverage availability. Nonetheless, based on the data provided, a probability of approximately 0.37 accurately reflects the likelihood of a student receiving their preferred beverage under the current conditions.

References

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