Lesson video

Hi, my name is Mrs. Wheelhouse.

Welcome to today's lesson on using lists to display outcomes for two events.

This lesson falls in the unit: Probability, possible outcomes.

I absolutely love probability.

So I'm really looking forward to doing this lesson with you today.

Let's get started.

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

Let's get started.

For our lesson today, we're going to be using a keyword, which is "systematically." Now, when listing outcomes systematically, they're listed in such a way to ensure all outcomes are recorded.

I wonder what that's going to look like though practically.

So when we're actually doing it, we will see this in our lesson.

So don't worry if you're not too sure right now.

We've got three parts of today's lesson.

We're going to start with possible outcomes from a two-stage trial.

If we roll a fair six-sided dice, then the possible outcomes are 1, 2, 3, 4, 5, and 6.

If we were to flip a fair coin, then the possible outcomes are heads and tails.

If we were to randomly select a letter of the alphabet, then the possible outcomes are, well, the letters of the alphabet.

We can list the outcomes of a single stage trial relatively easily.

I mean, you saw us doing it there.

If we were to spin this spinner twice, what are the possible outcomes? Well, you could win the first time and win the second time.

You could lose both times.

You could lose the first time, win the second time, or win the first time and lose the second time.

What's about this spinner? If we were to spin this one twice, what would the possible outcomes be? Well, we could win, win; lose, lose; lose, win; or win, lose.

Aisha says, "The spinners are different.

Why are the outcomes the same?" And Laura points out that the spinners have the same outcomes, but the likelihood of the outcomes has changed.

And she's right because the sector for lose is now bigger than the sector for win.

Quick check: Which of the following spinners when spun twice, do not have a sample space of win, win; lose, lose; win, lose; and lose, win? Pause the video and make your choice now.

Welcome back.

Did you go for B? That's right.

Each spin has three possible outcomes rather than two, because draw is an option.

If we were to spin this spinner twice, what are the possible outcomes? Instead of having to write out, win, lose, and draw, let's instead do shorthand and use the letters W, L, and D.

So Aisha says, "This spinner is different in terms of its outcomes," Laura says, "Well, yes, because there's gonna be more possible outcomes here, 'cause we don't just have winning and losing.

There's now the option to draw as well." So our possible outcomes would be win, win; lose, lose; draw, draw; win, draw; lose, win; draw, lose; win, lose; draw, win; and lose, draw.

Woo, that was a lot.

Does it matter there are two win sectors on the spinner? Laura says, "Well, not for the possible outcomes." It just means the outcomes with win are more likely to be landed on, just because if we put the two sectors together, we can see it's a much bigger area than either of the others.

A quick check now.

A spinner is spun twice.

The possible outcomes are AA, BA, AB, and BB.

Which of these spinners could have been the one that was spun? Pause the video and make your choice now.

Welcome back.

What did you go for? You should have picked all of them because each spinner has two possible outcomes of A or B.

So when the trial, which is spinning it twice, is carried out, there are the four possible outcomes that you saw in the sample space.

Jacob is going to spin both spinner A and spinner B for his trial.

What are the possible outcomes that Jacob will get? Well, he could get B, D; A, C; A, B; A, A; B, C; B, A; A, D; and B, B.

(sighs) There's quite a lot of outcomes there.

If two people were playing rock, paper, scissors, can you think of a possible outcome to that game? If you're not too sure, maybe you could try playing rock, paper, scissors now and writing down what you see as a possible outcome.

So it could be that one person chooses paper and the other chooses rock.

One person could choose scissors, the other could choose paper.

They could both choose rock.

What about listing all the possible outcomes? Have a go at this now.

Welcome back.

Did you get them all? Well, our first person could choose rock, paper or scissors, and our second person could choose rock, paper or scissors.

We're gonna make this shorthand just so it's a little easier.

Let rock be R and paper be B and scissors be S.

So you can see here I've said if the first person chooses paper, second person could choose rock.

If it's just scissors, we could have had paper and we could have rock and rock.

They were the ones that I showed you earlier on.

But of course they're not the only combinations.

If I chose paper, the other person could have chosen scissors.

If I chose scissors, the other person could also have chosen scissors.

If I chose rock, second person might have done paper.

If I did scissors, the other person might have done rock.

And of course if I'd done paper, the person might have done paper.

Do you think I've got them all yet? Oh, well done if you spotted.

I haven't quite got them all.

There's still one more to go.

And that's if I choose rock and the other person chose scissors.

I've used the diagram to try and make sure I've got all the possible outcomes there.

"Hang on," says Jun.

"Aren't SP and PS the same outcome? I mean it's just scissors and paper, right?" "No," says Izzy, "Because they are the same combination, but not the same outcome." So we still have a combination of scissors and paper, but it does matter which person chose which.

It's now time for our first task.

On the screen, you can see two sets of cards.

Jacob has listed some of the possible outcomes when selecting one card from each set.

For Question 8, I'd like you to please to state which outcomes Jacob has missed from his list.

And then in part B, are there any outcomes that Jacob has duplicated? Pause the video while you have a go at this.

Welcome back.

Let's go through our answers now.

So what outcomes has Jacob missed from his list? Well, he's missed choosing A, when A is a heart, he's missed choosing B, if B is a club, he's missed choosing C, if C is a heart, he's missed choosing C, being a spade as well.

So actually Jacob missed quite a few there and he'd missed when D is a star.

What outcomes has Jacob duplicated? Can you see that he's got D paired with a heart twice? It's at the bottom of the second column and at the top of the fourth column.

Well done if you spotted that.

It's now time for the second part of our lesson and that's on systematic listing.

A restaurant has a two course set menu.

You select one from the starters and one from the main course section.

What are the possible two course meals you might get? Well, Andeep thinks I could have garlic mushrooms and a bacon cheeseburger.

I could have halloumi bites and vegetable curry.

But you notice how Andeep's not listed all these words out.

He's used short notation for it instead.

So you can see he's used the letters to represent which of the options he's choosing.

Well done, Andeep.

That looks a lot faster.

Sofia has listed out what she thinks are the different options and so has Alex.

Oh, there's quite a lot of lists there.

Are they all the same? It's really hard to tell.

Whose list do you think is the least systematic? So what I mean by that is, remember, is the least ordered.

Which one looks all jumbled up to you? And can you say why? Andeep's list is not systematic.

It jumps between the different starters and main courses.

It might mean that we miss some outcomes or that we duplicate some.

Why do you think Sophia and Alex's lists were better? So let's have a look at their lists.

What do you think makes them better? What can you spot maybe in each list? Well, Sophia has systematically found the outcomes for each starter.

In other words, she started with the garlic mushrooms and then she paired them with each of the mains.

So we had GB, GF, GV, so she kept the G the same.

Then she looked at the Halloumi bites and considered all the possible ways to pair a main with the Halloumi bites.

Alex systematically found the outcomes with each main.

So he started with the bacon cheeseburger and paired it with each starter.

Then he looked at the fish and chips and paired that with each starter.

And then he looked at the vegetable curry and paired that with each starter.

So both of these approaches are systematic.

Alex and Sophia both started with one outcome and considered all the different possible pairings before moving on to the next outcome.

Let's do a quick check on this.

Both spinners are to be spun.

Complete the list of outcomes, pause and do this now.

Welcome back.

What did you put in those four gaps? If you are being systematic, you probably put them in the order C1, C2, C3, C4.

It's now time for your second task, A fair six-sided dice, and the spinner shown are to be rolled and spun simultaneously.

I'd like you please to list all the possible outcomes systematically.

And then in part B, how many possible outcomes are there? For Question 2, we've got a fair coin and a fair six-sided dice, and they're gonna be flipped and rolled respectively, simultaneously.

Please list the possible outcomes systematically and tell me how many possible outcomes there are.

Pause while you do this.

Welcome back.

Let's look at Question 3.

Two spinners are going to be spun.

The possible outcomes are shown in the sample space.

Please complete the spinners, so that they could generate these possible outcomes.

Pause while you do this.

Welcome back.

Let's look at our answers.

So for the possible outcomes being listed systematically, I chose to fix the number and then pair that with the three different letters.

So I have 1A, 1B, 1C, 2A, 2B, 2C, 3A, 3B, 3C, 4A, 4B, 4C, 5A, 5B, 5 C, and 6A, 6B, 6C.

Now you might have chosen rather than fixing the number, to fix the letter, so you could have said A1, A2, A3, A4, A5, A6, B1, B2, B3, B4, B5, B6 C1, C2, C3, C4, C5, C6.

So, how many possible outcomes are there? Well, we can see there are 18, and this is quite easy to count.

But we could also deduce it by looking at the fact that was six different outcomes from the dice and three different outcomes from the spinner.

So 18 combinations in total.

For Question 2, you had to list the possible outcome systematically.

So you could have fixed the number on the dice and then done the possible outcomes for the coin.

So 1H, 1T, 2H, 2T, et cetera.

Or you could have fixed the outcome from the coin and consider the possible outcomes that pair with that from the dice.

So H1, H2, H3, H4, H5, H6 and T1, T2, T3, T4, T5, T6.

For B, how many possible outcomes are there? Well, there are 12.

And then Question 3, you had to complete the spinners.

Remember here are some examples.

Now it's up to you, but on the spinner where it's three, I've put A, B, C.

And on the spinner where there were four sections, I've written 1, 2, 3, and made a note that one of the numbers has to be repeated in the fourth sector.

Now you could have swapped the letters and the numbers around and put 1, 2, 3 on the first spinner and A, B, C with one letter repeated on the second spinner.

Time for the third part of our lesson.

And that's listing outcomes of two events.

If this spinner is spun, the possible outcomes are 1, 2, 3, 4, and 5.

Izzy and Lucas are playing a game.

Izzy gets a point if it lands on a prime number and Lucas gets a point if it lands on an odd number.

So from the sample space, which outcomes would form parts of the following events? So which outcomes lead to event one where Izzy gets a point? That's right, it's 2, 3 and 5.

Because they are the only prime numbers on the spinner.

In event two, Lucas gets a point, remember, if it lands on an odd number.

Which outcomes are going to lead to Lucas getting a point? That's right.

It's 1 and 3 and 5.

So the combined event that either Izzy or Lucas gets a point has which outcomes? That's right.

It's 1, 2, 3, and 5.

Because if it's a 1 Lucas gets a point.

2, Izzy gets a point, and 3 and 5, they both get points.

What about the combined event that both Izzy and Lucas get a point? Which outcomes would work now? That's right.

It's just 3 and 5.

'Cause we want 'em both to get a point.

What about the outcomes that fall in the event where only Izzy gets a point? Which outcomes do that? That's right.

It's just 2.

Quick check now.

Izzy and Lucas are playing the game and it's the same game.

So Izzy gets a point if it lands on a prime number and Lucas gets a point if it lands on the odd number from the sample space, which outcomes would form part of the event that neither Izzy nor Lucas receive a point? Pause the video while you write these down.

Welcome back.

What did you put? Well, the only outcome that is not prime and is not odd is 4.

So it's the only one that is going to form part of the event that neither Izzy nor Lucas receive a point.

If this spinner is spun, the possible outcomes are 3, 4, 6, 8, 12, 15, 24 and 30.

Sophia and Alex are playing a game and Sofia gets a point if it lands on a factor of 24 and Alex gets a point, if it lands on a multiple of 3.

We can list the outcomes that would give Sophia a point.

Remember she gets a point, she's got a factor of 24, so that's 3, 4, 6, 8, 12, and 24.

And we can list the outcomes that would give Alex a point.

Remember he wants multiples of 3 so 3, 6, 12, 15, 24, and 30.

So here are the outcomes that lead to Sophia getting a point and the ones that lead to Alex getting a point.

So which outcomes give both Sophia and Alex a point? That's right.

It's the ones that are common to both sets of outcomes.

So 3, 6, 12, and 24.

Which outcomes give neither Sophia nor Alex a point? That's right.

There are no outcomes that either Sophia or Alex do not have in their sets.

In other words, there's nothing.

But can you see that symbol? That symbol means it's the empty set.

In other words, there's nothing there.

I couldn't put a zero because zero sometimes is an outcome.

So I'm using that special symbol to show there's nothing there.

A fair six-sided dice is rolled.

Which list shows the outcomes for rolling an even number and a factor of 20? Pause and make your choice.

Welcome back.

Which one did you go for? That's right, it should be B.

A is the list of outcomes for even numbers or factors of 20 and C is the list of outcomes that are neither even numbers nor factors of 20.

Time now for your final task.

Laura and Andeep are playing a game using this spinner.

Now Laura wins a point if it lands on a factor of 10 and Andeep wins a point if it lands on a prime number.

Please complete each of the questions here so you'll be listing outcomes for various events.

Pause and do this now.

Welcome back.

Let's see how you got on.

For 1A, you had to list the outcomes that win Laura a point, and that would be 1, 2, 5.

In B, for Andeep to win a point, the outcome has to be a 2, a 3, or a 5.

In C, For neither Laura nor Andeep to win has to be 4.

And the outcomes when Laura and Andeep both win had to be two and five.

And then the outcomes when Laura wins, but Andeep does not, is just 1.

Time to sort what we've learned today now.

Using systematic listing is more likely to lead to error-free lists than randomly listing outcomes.

The outcomes for two events can be listed separately as well as combined.

Well done.

You've worked really well today and I hope you've enjoyed learning how to list systematically and seeing how useful it can be when we are determining the set of possible outcomes.

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