If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains ***.kastatic.org** and ***.kasandbox.org** are unblocked.

Main content

Current time:0:00Total duration:6:23

AP.STATS:

UNC‑1 (EU)

, UNC‑1.P (LO)

, UNC‑1.P.3 (EK)

CCSS.Math: , so what I have here are 12 pieces of candy and the ones that are colored in brown are made out of have chocolate on the outside and the ones that have a C on them means that they have coconut on the inside so for example this one over here in the top left it's made out of chocolate on the outside but it doesn't have coconut on the inside well this one right over here does is chocolate on the outside and it has coconut on the inside while this one whoops I didn't want to do that while this one while this one right over here is does not have chocolate on the outside but it does have coconut on the inside and this one right over here has neither chocolate nor coconut and what I want to think about is ways to represent this information that we are looking at and one way to do it is using a Venn diagram so let me draw a Venn diagram so then diagram is one way to represent it and the way it's typically done the convention is that you would make a rectangle to represent the universe that you care about in this case it would be all the chocolates all the numbers inside of this should add up to the number of chocolates I have so it should add up to 12 so that's our universe right over here and then I'll draw circles to represent the sets that I care about so say for this one I care about the set of the things that have chocolate so I'll draw that with a circle it's not oftentimes you could draw them to scale but I'm not going to draw them to scale so that is my chocolate set chocolate that is my chocolate set and then I'll have a coconut set so coconut it's again not drawn to scale I'd remember awfully the same size but there's actually you can see the chocolate set is bigger than the coconut set in reality coconut so that and now we can fill in the different sections so how many of these things have chocolate but no coconut let's see we have 1 2 3 4 5 6 have chocolate but no coconut so that's going to be the X let me do that in a different color because I think the colors are important so let me do it in green so 1 2 3 4 5 and six so this section right over here is six and once again I'm not talking about the whole Brown thing I'm talking about just this area that I've shaded in green now how many have chocolate and coconut chocolate and coconut well that's going to be one two three so three of them have chocolate and coconut and notice that's this section here that's in the overlap between three of them go into both sets both categories these three have coconut and they have chocolate how many total have chocolate well six plus three nine how many have total have coconut well we're gonna have to figure that out in a second so how many have coconut but no chocolate well there's only one with coconut and no chocolate so that's that one right over there and that represents this area that I'm shading in and white so how many total coconut are there well one plus three or four and you see that one two three four and then the last thing we'd want to fill in because notice six plus three plus one only adds up to ten what about the other two well the other two are neither chocolate nor coconut actually let me color this so that's one - these are neither chocolate nor coconut and I could write these two right over here these are neither chocolate nor coconut so that's one way to represent to represent the information of what what how many chocolates how many coconuts and how many chocolate and coconuts and how many neither but there's other ways that we could do it another way to do it would be with a two-way table - a two-way table and on one axis say the vertical axis we could say let me write this so has chocolate has chocolate I'll write chalk for short and then I'll write no chocolate no chocolate chalk for short and then over here I could write coconut I went to that in white I got new tools and sometimes the color changing isn't so easy so this is coconut coconut and then over here alright no coconut no no cocoa nut no coconut and then let me make a little table let me make a table make it clear what I'm doing here so aligned there and aligned there and went on line over here as well and then I can just fill in the different things so how many have this cell right or this square this is going to represent the number that has coconut and chocolate coconut and chocolate well we already looked into that that's what one two three that's these three right over here so that's those three right over there this one right over here me is it has chocolate but it doesn't have coconut well that's this six right over here has chocolate but it doesn't have coconut so let me write this is that six right over there and then it has this this box would be it has coconut but no chocolate well how many is that well coconut no chocolate that's that one there and this one is going to be no coconut and no chocolate and we know what that's going to be no coconut and no no chocolate is going to be two and if we wanted to we could even throw in total totals over here we could write see let me just do that just for fun I could write total I could write total and if I total it vertically if I total it vertically so 3 plus 1 this is 4 6 plus 2 is 8 so this 4 is the total number that have coconut the boat the has chocolate and doesn't have chocolate and that's 3 plus 1 this 8 is a total that does not have the total that does not have coconut all right no coconuts the total of no coconut and that of course is going to be the 6 plus this 2 and we could total horizontally 3 plus 6 is 9 1 plus 2 is 3 what's this 9 that's a total amount of chocolate 6 plus 3 what's this 3 this is a total amount no chocolate that's this one plus 2 anyway hopefully you found that interesting this is just just different ways of representing the same information