# Reach with overlapping media audiences

Subject: Advertising and Public Relations

Exam: TEE

Reader: https://deep-learning-study-room.vercel.app/apr/#tee/practice/numbers/overlap

Canonical: https://deep-learning-study-room.vercel.app/read/apr/tee/practice/numbers--overlap/

Extra drills; no claim that these exact questions or allocated marks appeared in TEE

### Optional practice question. A campaign reaches 4,000 target members through radio and 3,000 through digital placements. Of these, 1,000 people are reached by both. The target population is 10,000. Find combined unique reach and percentage reach. [3 practice marks]

#### Answer

Authored illustration: these numbers were chosen to explain a faculty-note concept. No matching supplied-data question was found in the 14 recovered APR papers. Standalone calculation drills are optional practice; their marks are author-set.

## Given

| Radio reach | Digital reach | Overlap | Target |
| --- | --- | --- | --- |
| 4,000 | 3,000 | 1,000 | 10,000 |

## To find

Unduplicated combined reach and its percentage.

## Formula and why



$$
|A\cup B|=|A|+|B|-|A\cap B|
$$





$$
R_{\%}=\frac{|A\cup B|}{N}\times100
$$



The shared group appears once in each media count. Subtract it once so every person is counted exactly once.

## Step-by-step solution

#### Step 1. Add the two media counts



$$
4000+3000=7000
$$



#### Step 2. Remove the duplicate count



$$
7000-1000=6000\text{ unique people}
$$



#### Step 3. Divide by the target population



$$
6000\div10000=0.6
$$



#### Step 4. Express as a percentage



$$
0.6\times100=60\%
$$



**Final answer:** 6,000 unique people; 60% reach.

#### Practical interpretation · What the answer means

Adding media audiences without removing their overlap would overstate the number of different people reached.