Probability question

Question

A survey was done to see how many people visit the beach, go camping or go to the waterslides during the summer months. It was found that 35% went camping, 57% went to the beach and 20% went to the waterslides. 15% went camping & to the beach, 8% went to the beach & to the waterslides, 5% went camping & to the waterslides and 3% went to all three. Draw a Venn diagram to display the information and find the percent of the survey population that:

a) went to the beach or went to the slides.

b) went camping or went to the beach.

c) only went to one of the three locations.

d) did none of the three activities.

 

Answer 1

Draw three overlapping circles.  Label them beach, camping, waterslide.  Next to the labels, but NOT in the circles, write the percentages 57% (beach), 35% (camping), 20% (waterslide).

 

Notice that if you add all those percentages up, you have more than 100%.  That means you have overlap.

 

Using the information given in the problem:

Start in the very middle overlap of all three circles.  Put 3%

In the section between beach and waterslide but not in the very middle, put 8%.

In the section between beach and camping but not in the very middle, put 15%.

In the section between camping and waterslide, not in middle, put 5%.

 

Now you can figure out the beach only, camping only, and waterslide only pieces of the venn diagram.

57% total beach minus 15%, 3%, and 8% = 31% beach only

35% total camping minus 15%, 3%, and 5% = 12% camping only

20% total waterslide minus 8%, 3%, and 5% = 4% waterslide only

 

Now to answer the questions:

a)  beach or slides -- add up all percentages in the beach or slides circles

31% + 15% +3% + 8%+5% + 4% = 66%

 

b)  camping or beach

31% + 15% + 3% + 8% +12% + 5% = 74%

 

c)  only went to one of three locations -- count up the percentages in the beach only, camping only, waterslide only

31% + 12% + 4% = 47%

 

d)  none of the three activities -- add up ALL percentages in all circles and you should get 78%.

To find how many did none of the activities, subtract 78% from 100% = 22%