Lesson video

Hi, I'm Mrs. Wheelhouse, and welcome to today's lesson on using lists to display outcomes for more than two events.

This lesson falls within the unit Probability: possible outcomes.

Now I love probability, so I'm really looking forward to doing today's lesson with you.

Let's get started.

By the end of the day's lesson, you'll be able to systematically find all the possible outcomes for more than two events by listing them.

Now, just a quick reminder of some keywords.

When listing outcomes systematically, they're listed in such a way as to ensure all outcomes are recorded.

And that's gonna be really important in what we're doing today 'cause we're gonna be considering outcomes for more than two events.

So we've moved on, and that means it's gonna be a little bit more work than it was before.

Our lesson has two parts to it, and we're going to begin with part one on listing outcomes from a multi-stage trial.

If we were to spin this spinner three times, what are the possible outcomes? Well, we could win, win, win.

Aw, brilliant.

We could win, win, lose, we could win, lose, win, or we could win, lose, lose.

Do you think that's all of them? That's right.

Here it's nowhere near.

We could also lose, win, win, lose, win, lose, lose, lose, win, or lose, lose lose.

That's quite a lot, isn't it? Lucky there are only two outcomes.

Now this list of outcomes, they're all possible outcomes for all of these spinners, but all spinners look very different.

So how is this possible? That's right.

Each spinner has two outcomes, win or lose.

So there's only the likelihoods that changed, not the possible outcomes.

Now quick check, if all of these spinners are to be spun four times, which would have a different list of possible outcomes to the other two? Pause and make your choice now.

Welcome back.

Now you might initially have thought, "What's Mrs. Wheelhouse going on about? They've all got the same possible outcomes." I can clearly see there's an A on a purple background, a B on a greeny background, and a C on a blue background.

Obviously, they're all the same.

Did you spot that I'd been a little bit sneaky here? Did you spot that spinner C has a B on the blue background, not a C? And that means it only has two outcomes on this spinner, A or B, not A, B, C, which is what the other two spinners have.

Well done if I didn't catch you out.

Now Jun is going to spin these three different spinners.

Spinner 1 has the outcomes A, B, C, Spinner 2 has the outcomes plus and minus, and Spinner 3 has the outcomes X, Y, and Z.

Now, spinner one and spinner two can be combined to show the outcomes.

So if I just span those two spinners, I could get A being a plus or a minus.

I could get B being a plus or a minus, and I could get C with a plus or a minus.

By combining it like this, I can then write a list comparing the new Spinner 1/2 and Spinner 3.

I combined all three of those spinners into one mega spinner that shows all possible outcomes.

It's quite big, isn't it? And you can see, I've listed all the outcomes as well, and there's a lot there.

By doing it this way though, I've tried to ensure I'm systematically listing so that I can guarantee that I got all the outcomes.

Izzy says, "Does it not matter in which order the spinners were combined?" Oh, that's interesting, Izzy.

Does it matter? And you're right, it doesn't.

You can see that right there, there are 18 outcomes regardless of the order we create them in.

Now, what I'd like you to do is use my mega combined spinner here to complete the three spinners before they were combined.

Pause the video and do this now.

Welcome back.

Now, the first spinner had a plus and a minus on it, and that was complete.

So you only had to complete the other two.

You should have filled an M on the spinner that had a P and a B already on it, and three on the spinner that had the numbers one and five on.

It had to be this way round because of the way you can see our combinations in our mega spinner, you don't see an M ever paired with a P or a B, and that's because they're on the same spinner so those outcomes can't come up at the same time.

Let's consider this.

A fair six-sided dice is going to be rolled, and this spinner is going to be spun, and a fair coin is going to be flipped.

So what you can now see are the possible outcomes for each of these events.

So the possible outcomes of the dice are 1, 2, 3, 4, 5, 6, the possible outcomes of the spinner are A, B, C, and the possible outcomes of the coin are H and T, for heads and tails.

To list all of the possible outcomes of this multi-stage trial, we should try to be systematic.

So for instance, we could keep the outcome of the dice the same and then the spinner and then the coin.

What's that going to look like? Well, let's see.

I could start by keeping the dice value fixed, so it's one, and the spinner fix, that's A, and consider when I get heads, or consider when I get tails.

Right, that's all the possible combinations for, one, coming up on the dice, and A, coming up on the spinner, and then the coin showing whatever it shows.

So now, again, still keeping the dice value fixed, I'm gonna now consider what happens to the coin if my spin is shows B, and that's it could be heads or tails, and I'm gonna keep this process going.

So I'm gonna consider when it's C next, it could be heads or tails.

Notice how the one on the dice has not changed yet, and it didn't change because I had to go through all the spinner outcomes and all the various outcomes of the coin for each of the spinner outcomes.

Now I do the same list again, but this time, I'm starting with two on the dice.

And you can see, it's a very similar pattern to what I had before, but this time I'm just fixing the two.

And again, I'm then fixing the spinner, considering the two options on the coin, and then I change the spinner, and I consider the two outcomes of the coin.

But notice how the value of the dice stayed the same.

Can you spot a pattern here? That's one of the benefits of listing systematically is that we will start to see a pattern emerge.

There you go.

Can you see how it doesn't matter whether I consider the columns or I consider the rows, there's a pattern to both of them.

So if we consider the row, you can see that the value on the dice changed, but the spinner and the coin were the ones that were fixed, for that row at least.

And then here, for example, I changed all the heads to be tails, so I changed just one thing, because it was also going 1, 2, 3, 4, 5, 6 again.

And I follow this pattern all the way down.

Now, Sofia is going to complete her homework, tidy her bedroom, and practise playing her instrument.

Complete the list of possible orders she could do these three tasks in.

So I've put something for you.

What are the missing two, please? Pause and write this down.

Welcome back.

Did you spot what was missing? That's right.

She could do her instrument first, her homework, and then tidy her bedroom, or her instrument, tidy her bedroom, and homework.

Now you may arrange this to rand, and it's absolutely fine if you did.

Hm, let's consider this lock.

It needs three single digits.

We know the first digit is a multiple of three, the second digit is a factor of 20, and the third digit is an even number.

Now the first digit therefore has to either be a three, a six, or a nine.

The second digit has to be a one, a two, a four, or a five.

And the third digit has to be either 2, 4, 6, or 8.

What are the possible outcomes for the lock if we know it has to end with a two? Pause the video and write these down now.

Welcome back.

Did you get all of these? Now I've listed them systematically to make it very easy to check, so feel free to pause right now so you can check 'em against your list.

We've got a different look this time.

The first digit is one of the following outcomes, so it's a four and eight, the second digit has to be a one, a three, or a nine, and the third digit is either a zero or a seven.

Now Alex has already tried the following combinations with no success.

What other combinations does Alex need to try? Pause the video while you work this out.

Welcome back.

Did you spot that Alex has been systematic in what he's trying out? If you did, then it would be really quick and easy for you to work out what combinations Alex has left to try.

And that would be 890 and 897.

It's now time for your first task.

You'd need to do some revision.

So he uses three spinners to decide which subject, math, english, science, or geography, how long to spend on it, the duration, so 20 minutes or 60 minutes, and which resource, so Oak National Academy resources, flashcards, or books.

But I'd like you to write down all the possible outcomes for Jun's revision.

And then in part B, compare your list of possible outcomes to Jun's list of possible outcomes.

See if you can spot any differences.

Pause the video and do this now.

Welcome back.

In question 2, there's a restaurant where they have a fixed price three course menu.

Part A, write down all the possible outcomes that include ice cream as the dessert.

In part B, list all the possible outcomes that include vegetable curry as your main course.

And then for C, list all the possible outcomes that include garlic mushrooms as the starter and fruit salad as the dessert.

Pause and do this now.

Welcome back.

Let's go through question 1.

So part A, you had to write down all the possible outcomes for Jun's revision, and you'll see them all listed down here.

Now please do you feel free to pause so you can check this.

I have done this systematically, but you might have put yours in a different order.

So do you take the time to check you've got them all.

Part B now, you had to compare your list to Jun's list.

Now if you did that and you got yours right, you'll have noticed that Jun has missed doing science for an hour using flashcards.

So the SHF outcome was missing, and he's duplicated the STB, or science, 20 minutes, and books outcome.

Also, his list is not systematic, so apologies if it took a while to check.

Jun needs to be systematic in future when doing lists.

Question 2, write down all possible outcomes that include ice cream.

So you can see here, you could have had GCI, GFI, GVI, HCI, HFI, and HVI.

For B, you had to list all possible outcomes that included vegetable curry as the main course.

And luckily this time there were only four.

So GVI, HVI, GVS, and HVS.

Then part C, list all possible outcomes that include garlic mushrooms as the starter and fruit salad of the dessert.

Well, by fixing these two, it meant you could only vary the main.

So it could be GCS, GFS, or GVS.

While done if you've got this all right.

It's now time for part two of the lesson, and that's listing outcomes from more than two events.

So this spinner has the outcomes, 2, 3, 4, 8, 11, 13, 15, 16, 20, and 25.

And we've got three events listed here.

Event A is it's a prime, B, it's a non square number, and C, it's odd.

If we spin this spinner once, which of the possible outcomes would be outcomes of event A, B, and C? Well, here they are.

A could be 2, 3, 11, 13, B could be 2, 3, 8, 11, 13, 15, 20, and C could be 3, 11, 13, 15, and 25.

So we can see here that the possible outcomes that are outcomes of all three events, in other words, ones that are common to all three are 3, 11, and 13, because we can see them in all three lists.

What about now? So which of the possible outcomes would be outcomes of events A and B, but not C? Pause while you work this out.

Welcome back.

Did you spot that it's just two? Two is in both A and B, but is not in C.

So which possible outcomes would be outcomes of events B and C, but not event A? Did you spot? It's just 15.

15 is in the list for B and C, but not for A.

Let's do a quick check.

When this spinner is spun, the possible outcomes are 2, 4, 5, 7, 8, 10, 11, 14, 16, and 20.

List the outcomes that are even, factors of 28, and less than 10.

Pause and do this now.

Welcome back.

I'm gonna do this in a systematic way.

I'm gonna start with the outcomes that are even.

Well, from our list of outcomes, that's only 2, 4, 8, 10, 14, 16, and 20.

So I've reduced the possible outcomes.

In other words, I took my original list and I've cut out the ones that are not even.

I'm now gonna consider, of this list, which of these are factors of 28? So outcomes that are both even and factors of 28 are just 2, 4, and 14, because 8, 10, 16, and 20 are not factors of 28.

I'm now gonna consider of this group, which of these outcomes are less than 10? Well, that's just two and four.

By doing it this way, I've made sure that I've got all possible outcomes that are even, factors of 28, and less than 10.

10 pupils are asked whether they have ever visited France, whether they have been on an aeroplane before, and whether they have any siblings.

And you can see the set of outcomes for each event here.

First question for you is, what are the names of our 10 pupils? You should be quite familiar with them.

Pause while you write this down.

Now you might be quite familiar with them 'cause these are 10 Oak pupils.

We've got Andeep, Jun, Alex, Sam, Laura, Aisha, Lucas, Izzy, Sofia, and Jacob.

Which pupil has visited France, been on an aeroplane, and has siblings? Pause while you work this out.

Did you spot which pupil is in all three groups? That's right, it's Jun.

Jun visited France, been on aeroplane, and has siblings.

Which pupils do not have any siblings? That's Alex, Sam, Laura, and Aisha.

They're not outcomes of the event having siblings.

Quick check now.

Here is a pack of party hats.

Sofia would like a party hat that is striped, has a topper, and a string.

Which hats would satisfy Sofia's requirements? Pause the video while you write down the letters.

Welcome back.

Which ones did you go for? We should have picked hats D and F.

You can check that right now.

They're stripy, they have something on the top, and they have strings.

It's time now for your final task.

Question 1, Andeep, Izzy, and Lucas are playing a game using this spinner.

Andeep wins a point if the word starts with an M, Izzy wins a point if the word has four letters, and Lucas wins a point if the word ends in a vowel.

For part A, list the outcomes that get Andeep a point, B, list the outcomes that get Izzy a point, C, list the outcomes that get Lucas a point, in D, list the outcomes that get both Andeep and Izzy a point, in E, list the outcomes that get Izzy and Lucas a point, and then for F, list the outcome that gets all of them a point.

Pause while you work through this now.

Time for question 2.

10 animals are sorted into three categories, whether they are critically endangered, whether they are a mammal, and whether they live on land.

For part A, list all the land mammals that are critically endangered.

And for B, list all the mammals that are not critically endangered.

So remember, part A, I want all the land mammals that are critically endangered, and for B, the mammals that are not critically endangered.

Pause now while you work this out.

Welcome back.

Time to go through the answers.

For question 1, part A, list the outcomes that get Andeep point.

Remember, Andeep gets a point if the word starts with an M.

So that's mouse, menu, match, and milk.

Part B, Izzy gets a point if it's got four letters.

So that's menu, tree, ship, and milk.

In C, Lucas gets a point, remember, if the word ends in a vowel.

So menu, cello, tree, and mouse.

In D, we want the outcomes that get and Andeep and Izzy a point.

So remember, they've got to have four letters and start with letter M.

So that's just menu and milk.

in E, the outcomes that get Izzy and Lucas a appoint.

So four letters, end in a vowel, that's just menu and tree.

And then F, the outcome that gets all of them appoint is menu.

For question 2, you had to list the land mammals that are critically endangered.

Remember, they had to be in the set of animals that were on the land, the set of animals that were mammals, and the set of animals that are critically endangered.

So you should have the three you can see here.

And then part B, you want the mammals that are not critically endangered.

So again, you can see the list down here.

So to be mammals and not in the critically endangered set.

Well done if you've got these all right.

It's now time to sum up what we've learned today.

Outcomes for more than two events can be stated or listed.

When listing outcomes, it is useful to do it systematically to avoid duplicating outcomes or missing any out.

Well done, you've worked really well today.

I look forward to seeing you for more of our lessons on probability.