In a group of 60 people, 27 like coffee, 30 like tea, and some like both. If 5 people do not like either, how many like both coffee and tea?

Official Answer

Certainly, approaching a probability question like this one requires a methodical breakdown, ensuring that each part of the problem is carefully considered. Let's dive into how I would solve this, drawing upon my experience as a Data Scientist, where dealing with overlapping data sets is part of my daily routine.

Firstly, we know that the total number of people in the group is 60. Out of these, 5 people do not like either coffee or tea, which means 55 people like at least one of the two beverages. The problem also tells us that 27 people like coffee and 30 people like tea. At first glance, it might seem like simply adding these two numbers would give us the total number of beverage likers. However, this approach doesn't account for the overlap — people who like both coffee and tea.

To accurately find the number of people who like both, we apply the principle of inclusion-exclusion. This principle helps in solving problems involving overlapping sets and is a fundamental concept in probability and statistics, areas that are incredibly pertinent in data science.

So, applying this principle, the number of people who like both coffee and tea can be calculated as follows: - First, add the number of coffee likers to the number of tea likers: (27 + 30 = 57). - Then, subtract the total number of people who like at least one of the beverages (55, given by subtracting the 5 who don’t like either from the total group of 60) from this sum. This difference gives us the number of people counted twice because they like both beverages.

Thus, the calculation is (57 - 55 = 2).

Therefore, in the context of this problem, 2 people like both coffee and tea. This solution not only demonstrates a clear understanding of how to handle overlapping sets but also showcases an ability to apply theoretical knowledge to practical problems, a critical skill in data science. Whether it's analyzing user behavior, segmenting markets, or optimizing algorithms, the ability to dissect and solve complex problems with logical precision and clarity is invaluable.

In practical application, especially in data science, understanding the nuances of data overlap is crucial for accurate data analysis and interpretation. This kind of problem-solving approach not only helps in making informed decisions but also in designing algorithms and models that are both efficient and effective. It's a testament to the importance of foundational principles in tackling real-world challenges, ensuring that solutions are not just feasible but also grounded in solid, logical reasoning.