Venn diagram

[dcc3038026]

Using a Venn diagram to answer the question.

A survey of 131 college students was done to find out what elective courses they were taking. Let A = the set of those taking art; B = the set of those taking basket weaving; and C = the set of those taking canoeing. The study revealed the following information:
n(A) = 45; n(B) = 55; n(C) = 40;
n(A ? B) = 12; n(A ? C) = 15; n(B ? C) = 23;
n(A ? B ? C) = 2.
How many students were not taking any of these electives?

 

[Deleted member 4993]

Using a Venn diagram to answer the question.

A survey of 131 college students was done to find out what elective courses they were taking. Let A = the set of those taking art; B = the set of those taking basket weaving; and C = the set of those taking canoeing. The study revealed the following information:
n(A) = 45; n(B) = 55; n(C) = 40;
n(A ? B) = 12; n(A ? C) = 15; n(B ? C) = 23;
n(A ? B ? C) = 2.
How many students were not taking any of these electives?

Please share with us your work/thoughts - so that we know where to begin to help you.

 

[dcc3038026]

Okay....... Here is my work, but its not right...... Please help?
Dcc

Total Number of students = 131
A= arts
B= basket weaving
C = Canoeing


Total A = 45
Total B = 55
Total C = 40

n(A ? B) = 12;
n(A ? C) = 15;
n(B ? C) = 23;

n(A ? B ? C) = 2.

Solution:

First we have to find how many students are taking only one elective
Students who are only taking Arts = 45 - 12- 15 - 2
= 16
Students who are only taking Basket weaving= 55 - 12- 23 - 2
= 18
Students who are only taking Canoeing = 40 - 15 - 23 - 2
= 0

So total students who are taking electives are = only taking A + only taking B + only taking C + taking A&B + taking A&C + taking B&C + taking A&B&C

= 16 +18 +0 + 12 + 15 + 23 + 2
= 86

So people who are not Taking any Electives = Total Student - Students who are taking Electives
= 131 - 86
= 45

 

[Deleted member 4993]

Using a Venn diagram to answer the question.

A survey of 131 college students was done to find out what elective courses they were taking. Let A = the set of those taking art; B = the set of those taking basket weaving; and C = the set of those taking canoeing. The study revealed the following information:
n(A) = 45; n(B) = 55; n(C) = 40;
n(A ? B) = 12; n(A ? C) = 15; n(B ? C) = 23;
n(A ? B ? C) = 2.
How many students were not taking any of these electives?

# of students taking at least one of those three electives = (45+55+40) - (12+15+23) + 2 = 92

# of students not taking any of those electives = 131 - 92 = ???

 

[Mrspi]

Using a Venn diagram to answer the question.

A survey of 131 college students was done to find out what elective courses they were taking. Let A = the set of those taking art; B = the set of those taking basket weaving; and C = the set of those taking canoeing. The study revealed the following information:
n(A) = 45; n(B) = 55; n(C) = 40;
n(A ? B) = 12; n(A ? C) = 15; n(B ? C) = 23;
n(A ? B ? C) = 2.
How many students were not taking any of these electives?

Since your topic is "venn diagram," I wonder if you DREW a Venn diagram.

You have three subjects taken...so I'd draw a big rectangle, with 3 intersecting circles inside it. The "big rectangle" is the "universe," or all students surveyed.

The three circles (each of which intersects the others) can be labeled A (taking art), B (taking basketweaving) and C (taking canoeing).

The region common to all three circles represents the number of students taking all three subjects.

N(A and B and C) is 2...so that number goes into the area common to all three circles.

Work your way OUT from that...

Here's a website with a Venn diagram for a situation similar to yours:

http://www.google.com/imgres?imgurl=htt ... image&cd=1

Start in "the middle." Then work your way towards the outside of the Venn diagram.

I hope this helps you.