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Hello, and welcome to the last lesson of this unit with me, Miss Oreyomi.

Today's lesson is going to be adding up everything we've done with Venn diagrams and just making sure we're very confident when we're working with this.

So you would be needing a paper and a pen for this lesson or something that you can write on and with also, should you need to put your phone on silence or get into a space that has got less noise and distraction then please do so for the duration of this lesson.

So pause the screen now, if you need to get your equipment, and also if you need to put yourself in a space with less those are distraction.

And when you're done, press play to begin the lesson.

Okay, let's think about our try this task.

The Venn diagram shows information about bikes in a bike shed.

This line, this symbol is meant to be the universal dataset for the bikes.

So we've got 150 bikes in a bike shed.

This B represents number of bikes that are black, and this C represents the number of bikes that are made in China and well, 68 means bikes are not black, nor were they made in China.

How would you go about getting values for each set? So think about it.

How would you go about getting values for each set? So pause the video and have a go at this and then resume, once you think you're done, and we can proceed with a lesson.

Okay, well, hopefully your brain is thinking, this is a probability question, an algebra question in a Venn diagram.

So I want to work out well, the probability or the answer, the number in each set.

But I have a specific question here.

Work out the probability that a bike is black.

Well, I know that the total number of bikes in the shed is 150.

So 150 must be equal to everything in my region, in my Venn diagram.

So it's 2x+5+x-7+21+68, 2x+x is 3x.

And then if I add my numbers together, so positive five x subtract seven plus 21 plus 68.

I get 87.

So 150 is equal to 87.

If I take away 87 from both sides, I am left with 63=3x and x=21 How can I work out the probability that the bike is black then? Well, I simply substitute my value of x into this.

So it's going to be two times 21 plus five.

And that should give me 47.

And I'm going to add that then to 21, takeaway seven, which is 14.

So my total answer is 61.

So work out the probability that the bike is black, is 61 over 150.

Have a go at this, in a class of 24 students, 12 students play hockey, 30 students play badminton, and four students don't play either of those sports.

Represent this information on a Venn diagram and work out the probability that the student only plays badminton.

So you're now trying to draw in your knowledge from the previous lessons to do this question.

So pause the video and attempt this task.

Once you're done, press play to continue.

Okay, I'm going to try and draw my Venn diagram over here.

I've got 24 students.

So I've got set one and set two, H for hockey and B for badminton.

I am told that 24 don't play either sports.

That is not true.

I am told that four students play neither sports.

So four is going to go there.

Now, what is the remaining, what number do I have to fill in the rest of my sets? Well, was going to be 24, takeaway four, which is 20.

However, at the moment I have more than 20, I have 25.

Don't hide, don't hide, because 12 plus 13 is 25.

So I am going to subtract that and I have five.

So my middle intersection is going to be five.

Cause it's the access it's showing me that five students play both hockey and badminton.

So five is here.

Well, if the total number of students who play hockey is 12.

This is going to be seven.

And they are the total number of students who play badminton is 13.

So this is going to be eight.

Work out the probability that the student only plays badminton.

Well, it's going to be eight over 24.

So it doesn't count this five.

Cause this five students also play hockey.

So it's going to be eight over 24.

It is now time for your independent task.

So like I said, this lesson is drawing on everything you've learned so far.

So it gives you, this gives you an opportunity to recap your knowledge on Venn diagrams. So pause the video and attempt all the questions on your screen.

Once you're done, press play, and we would go over the answers together.

So pause the video now and attempt the questions on your worksheet.

Okay, welcome back.

I wonder how you got on with your task.

I hope you are able to answer every question.

Let's go over question one.

There are 110 teachers in a school, 90 students, 90 teachers like skittles, 41 teachers like smarties and 25 teachers like both skittles and smarties.

So we're starting with the 25 in the middle of our Venn diagram.

Since I've got 25 here, I would need 65 to be in this region for it to add up to 90.

And I would need 16 to be in this region for it to add up to 41.

And then I will subtract 110 from 106 to get four.

So four teachers, neither like smarties or skittles.

Next question here is a Venn diagram.

Write down the numbers that are in set A and A intersection B.

This is going to be five, A union B.

So we're right in the numbers 10, four, 16, five, 11, eight and 15.

So 10, four, 16, five, 11, eight and 15.

Now, I want the probability of A compliment intersection B.

So I've started by drawing my A compliment over here.

So if I shade in my A compliment, this is what it's going to look like.

If I shade in B, this is what it's going to look like.

So A compliment intersection B is asking for what did they both share? What do these regions both share? Well, it's going to be this region here.

So what is the probability that I pick a number from this region? Well, it's going to be three 'cause there are only three numbers in this region over one, two, three, four, five, so three over eight.

All right, so this question is asking you for your probability.

So it needs to be either a fraction decimal or percentage.

And then a and b is just asking you to write the numbers in the set.

So check in to make sure that yours is correct.

I started with this to here cause he gave me the most information.

So I filled in the overlap for all three.

And then I worked my way out, worked my way inside from the outside in and the number of students that don't do, either law engineering or PE is 144.

Find the probability that a student selected at random studies, at least one of the three subjects.

Well, that's all of this, isn't it? That's the same as saying L, the probability of L union E union P.

So it's 106 over 250 that the students studies no more than one subject.

We're looking at this 40, this four and this 23, because they don't study anymore.

They simply study PE engineering and law.

So we add them together and we get 67 over the total, which is 270.

The probability of is that the students studies law and engineering, but not PE.

Well, it's just 19 because law and engineering is this intersect over here.

Given that a student studies PE.

So my given is that they study PE.

Find the probability that they study engineering.

So I want to find the probability of P dash PE.

So the region of PE is here.

And if I add all my values together, I would get 43.

So out of these 43 students, how many students study engineering? Well, these two, they study law, engineering and physics, but they study engineering and they also study PE and one is study engineering others, they also study PE.

So it's going to be three over 43.

Okay, your explore task.

How many integers between the number one and 1200 are not multiples of the numbers two, three, and five? So you need to draw three sets in your Venn diagram and how many integers between the number one and 1,200 are not multiples of any of the numbers, two, three or five.

So pause your video now and attempt the task and see how you get on, and then press play when you finish exploring your task.

We've now reached the end of today's lesson.

Not only that we've also reached the end of the unit.

So make sure you complete the quiz to check how much you've learned during this unit.

And I hope you have a lovely time.

Goodbye.