Question

Two hundred sixty-three TCC faculty members were surveyed regarding their plans for the upcoming weekend. The results were as follows:132plan to grade papers109plan to attend a football game96plan to do household chores28plan to grade papers and attend a football game53plan to grade papers and do household chores35plan to attend a football game and do household chores8plan to grade papers, attend a football game, and do household choresHow many planned to only grade papers?How many planned to grade papers or do household chores?How many did not plan to do any of these activities?How many planned to do at lease two of these activities?How many planned to attend a football game and do household chores, but did not have any plans to grade?How many planned to attend a football game or grade papers, but did not plan to do household chores?How many planned to do at most one of these activities?

Answer 1

ANSWERS

• Only grade papers: ,54

,

• Grade papers or do household chores: ,175

,

• Not do any of these: ,34

,

• At least two of these: ,100

,

• Attend football game ,and, household chores, but not grade papers: ,27

,

• Attend football game ,or, grade paper, but not do household chores:, 133

,

• At most one of these:, 163

Step-by-step explanation

We can put all the given information in a Venn Diagram. We have to draw three circles representing the three activities mentioned: attend a football game, do household chores, and grade papers.

We know that 8 people planned to do all three activities, so to each number of people doing at least one of these, we have to subtract 8. Then, to the total of each activity, we have to subtract the number of people who do more than one. We have the diagram:

With this diagram, we can answer all the questions.

The number of people that only planned to grade papers is 54 since the rest also planned to do other activities.

The number of people that planned to grade papers or do household chores is 75:

`59+16+27+45+8+20=175`

In total 263 faculty members were surveyed, so the difference between that and the number of people in the diagram is the number of people that did not plan to do any of these activities,

`263-(54+59+16+20+27+45+8)=263-229=34`

Hence, 34 people did not plan to do any of these activities.

Now, we have to find the number of people that planned to do two or three activities. This is the sum of the numbers in the intersections,

`27+20+45+8=100`

So, 100 people planned to do at least two of these activities.

The number of people that planned to go to a football game and do household chores, but not grade papers is 27.

Similarly, the number of people that plan to attend a football game or grade papers, but not do household chores is,

`54+59+20=133`

So, 133 people planned to attend a football game or grade papers, but not do household chores.

Finally, the number of people who planned to do at most one of these activities is the people who planned to do only one or the ones that planned to do any of these,

`54+59+16+34=163`

Hence, 163 people planned to do at most one of these activities.