Two hundred fifty-nine TCC faculty members were surveyed regarding their plans for the upcoming weekend. The results were as follows:
128 plan to grade papers
126 plan to attend a football game
110 plan to do household chores
29 plan to grade papers and attend a football game
67 plan to grade papers and do household chores
42 plan to attend a football game and do household chores
14 plan to grade papers, attend a football game, and do household chores
Sketch a Venn diagram and answer the questions below.

papers
game
chores
U
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How many planned to only grade papers?
How many planned to grade papers or do household chores?

Incorrect
How many did not plan to do any of these activities?
How many planned to do at least 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?
28
Incorrect
How many planned to do at most one of these activities?

Question

Answered

Answer :

FICHOHIN FICHOHIN · Answer 1

The Venn diagram is best for representing information of these sort. The Venn diagram is attached and the answers to the questions are :

Let :

Attend football game = F

Grade paper = P

Household chores = H

FnHnP = 14

FnP only = 29 - 14 = 15

FnH only = 42 - 14 = 28

PnH only = 67 - 14 = 53

From the Venn diagram attached :

The number who planned to grade papers only :

P only = 128 - (15 + 14 + 53) = 46

Number who plan to grade papers or do household Chores:

(FnP)only + (FnPnH) + (PnH)only + (FnH)only + P only + H only

(15 + 14 + 53 + 28 + 15 + 46) = 171

Number who did not plan to do any of the activities :

250 - (69 + 15 + 46 + 28 + 14 + 53 + 15) = 10

Number who planned to do atleast 2 activities :

(FnP)only + (FnPnH) + (PnH)only + (FnH)only

15 + 14 + 53 + 28 = 110

Attend football game and do house chores only :

FnH only = 42 - 14 = 28

Attend football or grade only :

(F only + P only + FnP only )

69 + 46 + 15 = 130

At most one of the activities :

F only + P only + H only + None of the activities

(69 + 46 + 15 + 10) = 140

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