Really Need Help with this venn diagram!

1. May 16, 2004

kray

Hi everyone, i've got a test tomorrow, and i've no idea how to do this question;

If someone could please do a step by step guide how to do this, it would be great.

Thanks very much.

Last edited by a moderator: May 1, 2017
2. May 16, 2004

Staff: Mentor

My first question is: do you know what those symbols mean? I'll translate: find the probability of being within either A or not-B (or both).

Then realize that the three numbers (and corresponding areas on the diagram) represent the entire universe: they add to 50. So... what's in A? what's not in B (that's not-B)? What's in either A or not-B? Get it?

Edit: I misread the diagram: the number 50 in the diagram represents the area outside of the overlapping ovals. Thus the universe = 50 + 50 = 100.

Last edited: May 16, 2004
3. May 16, 2004

Gokul43201

Staff Emeritus
I believe there's an additional 50 outside the sets A and B. So n(U) = 100. N(A) = 28. n(-A ^ -B) = 50. So that gives you one of the specified answers.

4. May 16, 2004

kray

Cheers guys,

I understand what the symbols mean, i just cannot understand how this has been done.

p.s the answer comes out to D> 42

I've tried for hours, and nothing i know gets this answer.

A misprint maybe? :tongue2:

5. May 16, 2004

Staff: Mentor

It's no misprint. (You mean 42/50, I presume.)

I goofed before. Gokul43201 is correct: that 50 refers to the area outside the overlapping ovals. Thus the total universe is 100, not 50. (Shame on me. :uhh: )

The way to solve these things is to take a pencil and mark every section of the diagram that meets the criteria. Then just add the numbers. Start with everything that is not-B.

6. May 17, 2004

HallsofIvy

Staff Emeritus
However, Gokul43201's answer is incorrect. D is, in fact, the correct answer.

As Doc Al said, Add up all things that are not in B (that are not B), then add those that happen to be in both A and B. (Hint: there is a single number in your picture that gives all things that are NOT in "A or not B"- you can just subtract that from 100 to get the number you want). Since the universe is 100, divide by 100. You will need to reduce the fraction to get the answer given.