## Venn Diagram: In a survey of 75 resorts, it was reported....

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Psv11
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### Venn Diagram: In a survey of 75 resorts, it was reported....

In a survey of 75 resorts, it was reported that:

45 provided refrigerators in the guest rooms
37 provided laundry services
23 provided refrigerators in the guest rooms and laundry services
29 provided refrigerators in the guest rooms and business centers
21 provided laundry services and business centers
12 provided all three features

Construct a Venn diagram and use it to answer the following questions:

(a) How many of the resorts provided only refrigerators in the guest rooms?
(b) How many of the resorts provided exactly one of the features?
(c) How many of the resorts provided at least one of the features?
(d) How many of the resorts provided exactly two of the features?
(e) How many of the resorts provided none of the features?

I'm having problems with this problem, any help would be greatful, the drawing of the diagram is getting to me.

stapel_eliz
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Joined: Mon Dec 08, 2008 4:22 pm
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Psv11 wrote:...the drawing of the diagram is getting to me.

To draw the diagram, just draw three overlapping circles.

Psv11 wrote:In a survey of 75 resorts, it was reported that:

45 provided refrigerators in the guest rooms
37 provided laundry services
23 provided refrigerators in the guest rooms and laundry services
29 provided refrigerators in the guest rooms and business centers
21 provided laundry services and business centers
12 provided all three features

You have three things to consider: fridges, laundry, and business centers. So label one circle "fridge = 45", another circle "laundry = 37", and the third circle "business center = 44".

Since twelve "provided all three", put "12" in the central overlap. (For a demonstration, try here.)

Since twenty-one did "laundry" and "business center", subtract the "all three" value from 21, and put the result in the overlap just between the "laundry" and "business center" circles. Do the same sort of thing with the 29 and the 23.

You now have all of the overlap values, and the total values. Subtract the overlap values from the total values to find the "only" values. Place the values in the non-overlapping portions of the circles.

Note that there are a total of seventy-five resorts. Add up the numbers from all the portions of the three circles. If this total is less than seventy-five, then put the difference outside the circles but inside the rectangle; this value represents "none".

Then read off the values from the picture to answer the exercise questions.