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In a survey, 70% of those surveyed owned...

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?

A

`25%`

B

`20%`

C

`10%`

D

`5%`

Text Solution

AI Generated Solution

The correct Answer is:
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%**. ---
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% ...
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