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simonmagusflies

Member

Registered: 2021-05-23

Posts: 32

Venn diagram help

Problem: A cat has thirteen kittens. Eight of the kittens have white hair, six of the kittens have spots, and eight of the kittens have long tails. All of the kittens have at least one of these traits. One kitten is white with spots and a long tail. Three of the kittens are white with spots. Two kittens have spots and long tails. One kitten has white hair but does not have spots or a long tail.

a. Draw a Venn diagram for this problem.
b. How many kittens are white with long tails, but don't have spots?
My answer is 3.

I'm having a hard time wrapping my dull head around this one. So far, I have:
https://i.imgur.com/HrIVYmE.png

But it adds up to 12, not 13. I definitely have something wrong with the spots cats, it can't surely be 0 (maybe?), but it says 6 cats with spots and 3 + 1 + 2 = 6 which leaves no room for cats with just spots.

Please help me out, thanks.

Last edited by simonmagusflies (2021-06-03 16:40:46)

Bob

Administrator

Registered: 2010-06-20

Posts: 10,626

Re: Venn diagram help

hi simonmagusflies

I think I see the difficulty.  When it says "Three of the kittens are white with spots." that should include the cat you have already put in the centre place where all three circles overlap. So change the 3 where white intersects spots into a 2.  Similarly "Two kittens have spots and long tails." should be taken to mean including the centre place so change the 2 in the bottom intersection into a 1.

You should find it all works out then.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

simonmagusflies

Member

Registered: 2021-05-23

Posts: 32

Re: Venn diagram help

OK, I've fixed it, is this right?
https://i.imgur.com/Jd3lfS7.png

Bob

Administrator

Registered: 2010-06-20

Posts: 10,626

Re: Venn diagram help

Better but that diagram has not got n(white) = 8.  Have a look at the 3s on the diagram and make an adjustment.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

simonmagusflies

Member

Registered: 2021-05-23

Posts: 32

Re: Venn diagram help

Sorry if I'm being obtuse, but I can't really figure this out. If I change the 3 in long tails, long tails won't add up to 8 anymore? Do I up one of the threes? My brain is scrambled eggs right now, haha.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,626

Re: Venn diagram help

Rub out both 3s.

Then insert in white intersect long tails but not spots a correct number to make n(white) = 8

Then in only long tails a correct number to make n(long tails) = 8.

Final check: do the seven numbers add up to 13?

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

simonmagusflies

Member

Registered: 2021-05-23

Posts: 32

Re: Venn diagram help

4 in white intersect long tails and 2 in long tails? It adds up!! Thanks!

Bob

Administrator

Registered: 2010-06-20

Posts: 10,626

Re: Venn diagram help

Hurrah!  Well done!

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob