Children At A School Were Asked What They Prefer
The Children At A Certain School Were Asked What They Prefer To Drink
The children at a certain school were asked what they prefer to drink with their lunch, and the following table summarizes the children's responses:
| Drink | Percentage |
|-------------------|------------|
| Soft drinks | 43% |
| Milk/chocolate milk | 29% |
| Water | 10% |
| Tea | 2% |
| Other | 16% |
The school only serves milk, chocolate milk, or water with lunch. What is the probability that the first student in line for lunch will be served their preferred beverage with their lunch?
Paper For Above instruction
The problem presents data on children's beverage preferences at a school, with the percentages of children favoring various drinks. Importantly, the school supplies only three options: milk, chocolate milk, and water. To determine the probability that the first student in line will receive their preferred drink, we need to analyze the given preferences with respect to the limited menu.
First, we interpret the data. The percentages reflect the proportion of children who prefer each beverage: 43% favor soft drinks, 29% favor milk/chocolate milk, 10% prefer water, 2% like tea, and 16% prefer other beverages. Since only milk, chocolate milk, and water are served, the relevant preferences are:
- Milk/chocolate milk: 29%
- Water: 10%
Children who prefer soft drinks, tea, or other drinks will not be served their preferred beverage because the school does not serve these options. We focus on children whose preferred drinks are among the served options, specifically milk or water.
The question asks for the probability that the first student in line will be served their preferred beverage, which depends on whether their preferred drink falls within the options offered. Assuming that the preference of each child is independent and that students are randomly lined up, and that their preferences are representative of the overall percentages, the probability that the first child prefers one of the served beverages is the combined percentage of children preferring milk/chocolate milk or water. This sum is:
29% (milk/chocolate milk) + 10% (water) = 39%
Thus, there is a 39% chance that the first student prefers a beverage served at school and, therefore, will be served their preferred drink.
Given this, the probability that the first student will be served their preferred beverage with lunch—assuming they are among those whose preferences align with what's served—is 0.39 or 39%. Conversely, there is a 61% probability they prefer a drink not served, and therefore, they will not receive their preferred drink.
In conclusion, based on the provided preferences and offerings, the probability that the first student is served their preferred beverage is approximately 39%. This probability assumes uniform and independent preferences among students and no bias in the order students line up.
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