Sets, Relations & Functions
Practical Problems on Union and Intersection
Grade 11
Question:
<p>Two newspapers A and B are published in a city. It is known that 25% of the city population reads A and 20% reads B while 8% reads both A and B. Further, 30% of those who read A but not B look into advertisements and 40% of those who read B but not A also look into advertisements, while 50% of those who read both A and B look into advertisements. Then the percentage of the population who look into advertisements is:</p>
<p>13.9</p>
<p>12.8</p>
<p>13</p>
<p>13.5</p>
Step-by-Step Solution
Key Concept: Use set theory (inclusion-exclusion principle) to find disjoint regions of readers, then apply conditional probabilities to each region to find the total percentage looking at advertisements.
<p><strong>Step 1: Find the disjoint regions using set theory</strong></p><p>Let total population = 100</p><p>Read A = 25, Read B = 20, Read both A and B = 8</p><p>Read A but not B = 25 - 8 = 17</p><p>Read B but not A = 20 - 8 = 12</p><p>Read both A and B = 8</p><p><strong>Step 2: Find those looking at advertisements in each region</strong></p><p>From (A only): 30% of 17 = 0.30 × 17 = 5.1</p><p>From (B only): 40% of 12 = 0.40 × 12 = 4.8</p><p>From (both A and B): 50% of 8 = 0.50 × 8 = 4</p><p><strong>Step 3: Calculate total percentage</strong></p><p>Total looking at advertisements = 5.1 + 4.8 + 4 = 13.9%</p><p>∴ Answer: A (13.9% or approximately 14%)</p>
Correct Answer: A