In a group of 400 workers, 210 prefer tea, 180 prefer coffee, ... | Mathematics MCQ | Examoogle

Examoogle • User • info@examoogle.com • EE-2024-8821

Chapter 1 of 12 • Page 1 of 248🔒 Protected PDF • Watermarked

MathematicsSet Theory

In a group of 400 workers, 210 prefer tea, 180 prefer coffee, and 90 prefer both. How many workers prefer neither tea nor coffee?

100

120

110

Correct Answer

📐 MA • Math Direct FormulaMathematicsSet Theory

Option A

100

Quick Summary:

Use the formula $\text{Total} - (\text{Tea} + \text{Coffee} - \text{Both})$ . Just add the individual groups, subtract the intersection to find the union, and subtract that from the total population.

📐MAMath SolutionDirect Formula

📋 Given

Total workers = 400, workers who prefer tea = 210, workers who prefer coffee = 180, workers who prefer both = 90.

🔢 Formula Used

n(T∪C)=n(T)+n(C)−n(T∩C)n(T \cup C) = n(T) + n(C) - n(T \cap C)n(T∪C)=n(T)+n(C)−n(T∩C)

⚡ Exam Hall Shortcut / Speed Trick

Use the formula $\text{Total} - (\text{Tea} + \text{Coffee} - \text{Both})$ . Just add the individual groups, subtract the intersection to find the union, and subtract that from the total population.

⚠️ Common Student Trap / Pitfall

Many students subtract the intersection only once from the sum of the two groups, forgetting to account for the fact that those 90 people are counted twice in the tea and coffee groups.

📊 Diagram / Illustration

🔢 Step-by-Step Solution

Calculate the number of workers who prefer at least one drink

To find the number of workers who prefer tea or coffee, apply the Inclusion-Exclusion Principle: $n(T \cup C) = 210 + 180 - 90$ .

n(T∪C)=390−90=300n(T \cup C) = 390 - 90 = 300n(T∪C)=390−90=300

Calculate workers who prefer neither

Subtract the number of people who like at least one drink from the total number of workers: $\text{Neither} = \text{Total} - n(T \cup C)$ .

400−300=100400 - 300 = 100400−300=100

✅

A is correct because the number of workers preferring neither is calculated as 400 - 300 = 100.

Core Concepts Used

Click any tag to open in AI Tutor

Set Theory Inclusion-Exclusion Principle Venn Diagram Logic

💡 EXAM TIP

This concept is foundational for Probability problems involving 'A or B' events, where $P(A \cup B) = P(A) + P(B) - P(A \cap B)$ .

Was this solution helpful?

Discussion (0)

Loading discussion...

Prev Next

Correct Answer

Related Questions

Discussion (0)