200 kids were asked if they liked hb and hd.5% didn't like either.85% liked hb.23% liked hd. what % liked both

Question

this sounds really weird but sorry it's because i ran out of room! HB stands for Hamburger and HD stands for Hotdog! plz help me out i keep thinking im doing it wrong! thanx!

Answer 1

Okay. So let's look at what you have:

85% of the kids like hamburgers. That means 15% don't.
23% like hot dogs. That means 77% don't.
5% don't like anything.

Now, if 15% of the kids don't like hamburgers, but only 5% don't like ANYTHING, that tells us that 10% like hot dogs but not hamburgers.

Since 23% like hot dogs all together, and 10% like ONLY hot dogs, the other 13% must like BOTH hot dogs and hamburgers. And that's your answer!

You can check it, too. Since 77% don't like hot dogs, then 72% like hamburgers but not hot dogs. The difference between that and the 85% is (thankfully) 13% again. So it works out.

If it helps, you can think of it as a Venn diagram: (this will look horrible)
..___...__
/........\/......\
|.......(.).......|
.\___/\___/
..hb...hd....

Everything in the left circle (hamburgers) is 85%. Everything in the right circle (hot dogs) is 23%. They have an overlap (what you're trying to find) and an excluded area (the kids who like nothing) of 5%.

At any point, the whole picture has to be 100%. So if you remove one circle and the outside, you'll just have the crescent on the other circle. And that crescent is the kids who liked one thing but not another. See?

Answer 2

There is definately something wrong with your question 0.5% of 200 = 1 person, 0.85% = 1.7 people?

I am going to assume you mean 5% disliked both (10 kids), 85%liked Hamburgers(170 kids ), 23% liked Hotdogs(46).

190 kids liked either Hot dogs, Hamburgers or both (200-10)

If you made a set diagram, it will look like there is an overlap (170+46= 216), but there are only 190 kids that liked both

The overlap = 216-190 = 26

Answer 3

Since 5% didn't like either, that means the 95% must have liked one or the other or both.

This is what we know.

P(Like HB) = 85%
P(Like HD) = 13%
P(Like HB or Like HD) = 95%

Using the formula

P(A or B) = P(A) + P(B) - P(A and B)

We are looking for P(Like HB and Like HD), so plug in what you know and solve for P(Like HB and Like HD)

95% = 85% + 23% - P(Like HB and Like HD)
95% = 108% - P(Like HB and Like HD)
P(Like HB and Like HD) = 108% - 95% = 13%

So that means that 13% of the kids like both hamburgers and hot dogs.

Answer 4

If you add 85 and 23 you get 108. But only 95 liked one of the 2. So 13 are counted twice. That's it 13%

Answer 5

200 kids (100%)- 10 kids (5%) that didn't like either = 95%
85%+23%= 108%
108%-95%=13%
The answer is 13%.

Answer 6

5% of 200 is 10
85% of 200 is 170
23% of 200 is 46
170+46=216 (total votes)
216-190=26 (the overlap...total votes - kids who like one or the other)
so 26 like both
26/200 = .13 so 26 is 13% of 200
13% like both

Answer 7

13%

Answer 8

wait, it has to be 100%. lol! 8%above