Venn diagram solution

Question

Two hundred thirty-four TCC faculty members were surveyed regarding their plans for the upcoming weekend. The results were as follows:

108	plan to grade papers
112	plan to attend a football game
91	plan to do household chores
27	plan to grade papers and attend a football game
54	plan to grade papers and do household chores
30	plan to attend a football game and do household chores
10	plan to grade papers, attend a football game, and do household chores

Sketch a Venn diagram and answer the questions below.

How 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

you have to fill in the small section where all 3 overlap, and then go backwards!!!

10 goes in the small section where all three intersect

30 plan do to household chores or goto the football game, but that includes grading papers too....

so 30-10 = 20 shall do household chores or goto the football game but NOT grade papers

54 - 10 = 44 plan to grade papers and do household chores, but NOT goto the football game

27-10 = 17 plan to grade papers and goto the football game but NOT do household chores

91 plan to do household chores and 44+10+20 = 74 are already accounted for; that leaves 17 for

household chores only

112 plan to goto the football game and 17 + 10 + 20 = 47 are already accounted for; that leaves 65

for the football game only

108 plan to grade papers and 17 + 10 + 44 = 71 are already accounted for; that leaves 37 for

grading papers only

=============================================

37 only grade papers

44 grade papers and do household chores

24 non participants

91 doing at least 2 activities

102 will not grade papers

109 will not do household chores

119 will do only one activity