Question

1. A survey of 700 households revealed that 300 had only a TV, 100 had only a computer, and 100 had neither a TV nor a computer. How many households have both a TV and a computer?​ Solve using a Venn Diagram

Answer 1

By using a Venn Diagram and the principle of inclusion-exclusion, we find that 200 households surveyed have both a TV and a computer.

Step-by-step explanation:

To solve the problem using a Venn Diagram, we begin by drawing two intersecting circles, one for TV owners and one for computer owners. Next, we input the given information. We know there are 700 households in total. According to the survey, 300 households have only a TV and 100 have only a computer, while 100 have neither TV nor computer. To find how many households have both a TV and a computer, we use the principle of inclusion-exclusion.

First, we subtract the number of households with neither a TV nor a computer from the total number of households:

Total with either TV, computer, or both = 700 (total households) - 100 (neither) = 600

Next, we subtract the households that have only one of the two devices:

Total with both TV and computer = 600 (total with either or both) - 300 (only TV) - 100 (only computer)

Now we simply subtract:

600 - 300 - 100 = 200

Therefore, 200 households have both a TV and a computer.

Answer 2

A survey 700 household says that 300 had only a tv