In a survey, 70% of those surveyed owned a car and 75% of those surveyed owned a TV. If 55% owned both a car and a TV, what percent of those surveyed did not own either a car or a TV?

Options

A. `25%`
B. `20%`
C. `10%`
D. `5%`

Explanation

To solve the problem step by step, we can use the principle of inclusion-exclusion. Let’s denote the following:

- Let A be the set of people who own a car.
- Let B be the set of people who own a TV.
- The percentage of people who own a car (A) = 70%
- The percentage of people who own a TV (B) = 75%
- The percentage of people who own both a car and a TV (A ∩ B) = 55%

We want to find the percentage of people who do not own either a car or a TV.

### Step 1: Calculate the percentage of people who own either a car or a TV (A ∪ B)

Using the formula for the union of two sets:
\[ N(A \cup B) = N(A) + N(B) - N(A \cap B) \]

Substituting the values we have:
\[ N(A \cup B) = 70\% + 75\% - 55\% \]

### Step 2: Perform the calculation

Calculating the above expression:
\[ N(A \cup B) = 70 + 75 - 55 \]
\[ N(A \cup B) = 90\% \]

### Step 3: Calculate the percentage of people who do not own either a car or a TV

To find the percentage of people who do not own either a car or a TV, we subtract the percentage of people who own either a car or a TV from 100%:
\[ \text{Percentage who do not own either} = 100\% - N(A \cup B) \]
\[ \text{Percentage who do not own either} = 100\% - 90\% \]
\[ \text{Percentage who do not own either} = 10\% \]

### Final Answer

Thus, the percentage of those surveyed who did not own either a car or a TV is **10%**.

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