Survey Problems 5

>> Hi, this is Julie Harland and I'm YourMathGal. Please visit my website at yourmathgal.com where you could search for any of my videos organized by topic.   This is Survey Problems Part Five. We're going to create and use a venn diagram to answer survey problem where three sets are involved. So here's our problem. A survey about which of the three beverages, tea, coffee, milk, people drink daily reveal the following? Seven drink only coffee, so no coffee or-- I mean no tea or milk for that set of people right? 21 drink coffee. One drink only tea and milk. Six drink all three, four drink none of the three, 21 drink tea, 11 drink tea and coffee, nine drink neither coffee nor tea. So let's answer a couple of questions. How many people were surveyed? And how many drink only milk? Hopefully, if you've been watching my videos, you know, you can't just add those numbers up. Because there's some intersections going on et cetera. So, since we're talking about three different things, tea, coffee, and milk, let's do a venn diagram with three sets. [ Pause ] So we've got the inverse, so we've got tea, coffee, and milk. How about I let this be the tea, this be the coffee, and this be the milk. Now remember, tea, there's four regions here. Like over here, people only like tea that-- here's the intersection of people who like both tea and coffee. And then up in this little tiny piece here. These are the people who like tea and coffee that they didn't like milk et cetera. So, there's a lot going on here. So let's see if we can fill in. Seven drink only coffee. All right, so. Is there, it's not just one region here. Here's the coffee region, all four pieces. But where is the piece of region where they only drink coffee. Now I just need this part here, they're not part of the tea or milk. So I could fill that in and I've just used that to use that information.   Next, we've got the second clue. 21 drink coffee. Well, the coffee is made up of four pieces and I've only got one piece so far. So I'm not going to-- I know that all together, these four numbers have to add up to 21. So I'm not sure what I'm going to put here. I know that it gives-- these three numbers will add up to 14, right? 'Cause they're only added to seven, I'll get 21. But, I can't get no anymore than that quite yet. How about the next one? One drink only tea and milk. All right. So, let's look at tea and milk. Here's the intersection of tea and milk but this has only tea and milk. So that means not coffee right? So this is only tea and milk. I don't get it. They don't get to also drink coffee. So I can actually use that clue in when it's going to go just in that little region right there. Six drink all three. All right. So, what does that mean if you drink all three beverages? That's the intersection of all three of these sets right in the center. Six goes right in the center. So I've used this clue.   Four drink none of the three. All right. What does that mean if you didn't, if you're not in any of these sets, it means they're out here some place right? So there are four people that didn't drink any of those beverages on a daily basis. So use I'll use that clue. 21 drink tea. Okay, so let's see. And here's my set of, people that like tea. I've got two regions filled in but there's two regions left to fill in. So I can't fill that in. I wonder how to split it out so that all of these add up to 21. In fact if this is seven, it's going to be again with seven plus 14, I think is [inaudible]. So these three numbers have to add up to 14, but I don't know how to split it up. How about the people that like to drink tea and coffee? 11 drink tea and coffee. Okay, so we've looked at the intersection of tea and coffee which is right here. There's two pieces but one is filled in. So I know that together, this has to add up to 11. So there's six here, five has to be the piece that goes up here. So five and six, add up to 11 and I've just used that clue.   Right. The next one. Nine drink neither coffee nor tea. All right, what does that mean? They are not in this coffee circle and they're not in the tea circle either right, at all. So if you look at the coffee or tea circle, if we put them together, you've got all these. But notice, there are two pieces outside there. The people that only like milk and the people who didn't like anything. So be careful, all people want to put nine right here, that isn't going to work. 'Cause now you've got 13 that didn't like coffee or tea. So be careful, that's not nine. Together of these two pieces, I have to add up to nine. So if this is four, it' s just then it would have to be five, and I've just used that clue. All right. I've gone through and used all the clues I can so far. So let's go back up to see if we didn't finish filling the rest of this out. I've got the 21 who drink coffee. And notice, I filled in three of the four pieces so far. So I have 18, five, seven, and six add up to 18, and there's 21 total. So what's left here are these little piece. It's got to be three, now that adds up to 21.   So we've used that clue. Also, 21 drink tea. We're going to do the same thing. So we're looking at the set of people who like tea, we've got one, six, and five already I counted for. So 12 people are counted for. So 12 plus what? Nine, it would add up to 21. And now, I filled in all eight regions. So now, how are we going to answer the question? How may people were surveyed? So I would add all eight numbers you see here. So let's see, I've got 10, 20, 30-- wait a minute, I see 10, 20-- I think I've got 40. I see 40 but I'm going to double check that and you should too. 11, 14, 20-- yup I got 40 again. How many drink only milk? All right. Where is that going to be? Right in here. This five people who drink milk, they don't get-- you kind of include these people who also drink coffee and or tea. So we've got five. Now, the last thing to do is go back to-- with the, through all your clues and make sure those numbers still match up correctly. All right. Seven drink only coffee. All right. So let's go over here. Where is the people that drink only coffee? Right here. I do have seven. It looks good. So I check that off, yup, that work. 21 drink coffee. So now, look at the circle of the coffee, make sure that adds up to 21. And five, seven, six, and nine, you add up to 21, okay. Check that one. One drink only tea and milk. Right. So, only tea and milk, it means they both-- they like both tea and milk. So I have to look at here. But it says only, I don't get to include the coffee people. So that's the one, good. Six drink all three. That's the intersection of all three drinks that's in the center is six, it looks good. Four drink none of the three. Well that would be out here. And I've got four so that looks good. 21 drink tea. So you'll look in the set of people that drink tea and you add up these four numbers and that does add up to 21. It looks good.   11 drink tea and coffee. So now, we're going to look at the intersection of tea and coffee. So that's right here in the center. Five and six add up to 11. Good. And nine drink, neither coffee nor tea. Okay, so that includes the people that only like milk or didn't like any drink and that is the five plus four. So all those done. So our answer should be correct if we go back up. Let's check one more time, how many people are surveyed? You're going to add eight numbers, you should get 40. How many drink only milk? That's just these five people right here. And then you could, you know, I could ask a whole bunch of other questions as well. You could make up your own problems. These aren't so easy to make up. I'm not going to go over how I made them that, but you could try it on your own. See if you can give eight clues. Usually, the trick is, that, if you're going to have eight regions, usually, you're going to have to give eight clues. And we have to be kind of careful so you could fill in eventually, you know, at the beginning of this, at least, going to be just one specific place you could fill in, and work up through there. Right. So I suggest, that you take this exact same problem without the answer, without the venn diagram all on your own and try it, and see if you could get the answer. And let's just ask one more question just for fun.   How many did not drink milk? What would that be? I'm going to look at the milk circle, and look outside of that, and I've got nine, five, seven, and four. So that is, let's see, four and seven is 11, plus to nine, there's 25, I got 25. [ Pause ] Please visit my website at yourmathgal.com where you can view all of my videos which are organized by topic.