Lesson video

Hi, I'm Mrs. Wheelhouse, and welcome to today's lesson on the scale of likelihood.

Now, this is from the unit Probability: Possible Outcomes.

I absolutely love probability, so I'm really looking forward to exploring the scale of likelihoods with you today in our lesson.

Let's get started.

By the end of today's lesson, you'll be able to show the likelihood of an outcome on a scale.

We're gonna be looking at certain keywords today, so let's review them now.

An outcome is impossible if there is no possibility that it can happen.

An outcome is certain if it is guaranteed to happen.

And an outcome has an even chance if its likelihood of happening is the same as its likelihood of not happening.

So we're gonna be using those words, impossible, certain, and even chance, in our lesson today.

Our lesson has two parts to it, and we're gonna start by introducing the scale of likelihoods.

The likelihood of different events can be compared and represented on a scale of likelihoods, and you can see a scale on the screen now.

Events that are more likely to happen go further to the right on the scale, and events that are less likely to happen go further to the left of the scale.

So for example, the likelihood of different spinners landing on win can be represented on a scale of likelihoods.

Now, we used this keyword at the start of the lesson, and we said an outcome is impossible if there is no possibility it can happen.

So remember, less likely outcomes go to the left of the scale, which is why impossible is all the way to the left.

So for example, it's impossible for the spinner you can see now on the screen to land on win, and that's because the entire spinner says lose.

An outcome is certain if it is guaranteed to happen.

So let's have a look at one of those.

So it's certain that this spinner will land on win because as you can see, it's the only thing the spinner shows.

Now, we mentioned the phrase even chance, and we said an outcome has an even chance if its likelihood of happening is the same as its likelihood of not happening.

So let's have a look at what that might look like.

So for example, this spinner here.

There is an even chance that this spinner will land on win.

An outcome that has a greater chance of happening than not happening can be described as being likely.

So for example, with the spinner you can see now, it is likely that this spinner will land on win 'cause the sector for winning is bigger than the sector for losing.

An outcome that has a less chance of happening than not happening can be described as being unlikely.

So let's have a look.

It is unlikely that this spinner will land on win, and that's because the sector for lose is much bigger than the sector for win.

So Lucas is thinking about where the likelihood that this spinner lands on A will go on our scale.

Where do you think it might go? Lucas says, "I think it is an even chance because the spinner has an equal chance of landing on each letter." What do you think? Does that reasoning match up with our definition for even chance? Lucas is incorrect.

Can you work out why? That's right, equal chance is not the same as even chance.

There is an equal chance that the spinner lands on each letter because the sectors are all the same size and each sector has a unique letter.

But the likelihood that the spinner lands on A is less than the chance that it lands not on A.

So what do we mean by that? Well, if we take our spinner where each sector, remember, was the same size and we had our unique letters, A, B, C, there was an equal chance that it could land on A, B, or C.

So they were equally likely outcomes.

But when we consider the spinner landing on A and the spinner not landing on A, we don't have an even chance here.

So remember, the likelihood that it lands on A here is less than an even chance, so it is unlikely.

Andeep, Izzy, Jun, Laura, and Sam are playing a game that involves rolling a regular six-sided dice to determine if you can move.

Andeep can move his piece if he rolls an odd number.

Well, you can see here which numbers are odd.

That's one, three, and five.

So Andeep has an even chance of moving.

Izzy can move her piece if she rolls a seven.

So where would Izzy go on our scale? That's right, there are no outcomes that allow her to have seven, so it's impossible for her to move.

Jun can move his piece if he rolls an integer.

Oh, quick reminder here of what an integer is.

Can you remember? As soon as you know, you'll be able to work out where Jun will go on our scale.

That's right, all of these are integers, so Jun can definitely move.

In fact, his likelihood of moving is certain.

Now, where's Laura going to go? Well, she can move her piece if she rolls a multiple of three.

So would you say that's impossible, unlikely, even chance, likely, or certain? Well, there are only two outcomes out of the six that mean that Laura can move, so I'd say it's unlikely she's going to move because there is less chance she can move than there is chance she won't move.

Lastly, Sam.

Sam can move her piece if she rolls a factor of six.

So where do you think Sam's going to go on our scale? Well, there are four outcomes that allow Sam to move her piece.

So because there are more outcomes that allow her to move than outcomes that mean she doesn't move, it's likely that she's going to be able to move her piece.

Time for a quick check.

There is an even chance that this spinner that you can see here will land on 1.

Is that true or false? And then you need to justify your answer by either selecting A, the spinner is less likely to land on 1 than it is to land on a number that is not 1, or B, the spinner is equally likely to land on each number.

Pause and make your choice now.

Welcome back.

Which one did you go for? Well, you should have picked false.

There is not an even chance that the spinner will land on 1, and you needed to justify this by selecting A.

The spinner is less likely to land on 1 than it is to land on a number that is not 1.

All our sectors here are the same size, and there is only one sector that shows 1 and three sectors that show numbers that are not 1.

What about this spinner? So same spinner again, but different statement.

There is an even chance that the spinner lands on an odd number.

Is that true or false? And then choose the statement that justifies your selection.

So either A, the spinner is equally likely to land on an odd number as it is to land on a number that is not odd, or B, outcomes that are equally likely never have an even chance.

Pause and make your choice now.

Welcome back.

What did you go for? Well, you should have said it's true, and the reason it's true is because the spinner is equally likely to land on an odd number as it is to land a number that is not odd.

We have two odd numbers, two even numbers, and the sectors that are odd are the same size as the sectors that are even.

It's time for your first task.

For each spinner, write down whether the likelihood of it landing on win is impossible, unlikely, even chance, likely, or certain.

Remember, we're considering the likelihood of the spinner landing on win.

Pause the video and have a go at this now.

Welcome back.

For question two, we've got Aisha, Izzy, Jacob, Lucas, and Sofia, and they're playing a game that involves rolling a regular six-sided dice.

Determine if they can move.

The information below shows what each person needs to roll in order to move their piece forward.

So for Aisha, she needs a factor of 24.

Izzy needs a multiple of 1.

Jacob needs a factor of 25.

Sofia needs a non-integer result.

And Lucas needs a prime number.

Represent the likelihood of each person moving their piece on the scale of likelihoods by writing the first letter of the name in the correct space.

Pause and do this now.

Welcome back.

Let's go through and mark these.

So for question one, for each spinner, you had to write down whether the likelihood of it landing on win is impossible, unlikely, an even chance, likely, or certain.

Well, for A, it's certain.

The only options are winning, so it's certain I'm going to win.

For B, it's likely I'll win.

You may even have wanted to go as far as to say it's very likely I'll win, and I can understand that.

But you just needed to write likely.

For C, it's unlikely I'm going to win.

The sector for losing is really big.

For D, it's impossible for me to win.

There's no outcome that says win there at all.

For E, there's an even chance.

For F, it's unlikely that I'm going to win.

For G, careful looking there, but it is likely.

There are more wins than loses, and all our sectors are the same size.

For H, there's an even chance.

And then for I, it's unlikely I'll win.

Well done if you got those all right.

Question two, you had to represent the likelihood of each person moving their piece on the scale of likelihoods.

Let's see where our Oak children should go.

So for Aisha, it's likely she'll be able to move, but for example, the number 5 is not a factor of 24, and that's why it cannot be certain for Aisha.

But there are lots of numbers on our dice that are factors of 24.

In fact, 1, 2, 3, 4, and 6 are all factors of 24.

So it's only 5 that stops Aisha moving.

Izzy needs a multiple of 1, so it's certain that she's going to move because all of the numbers on a dice are multiples of 1.

Now, Jacob wants a factor of 25, so it's unlikely he'll move because 1 and 5 are factors of 25, but they're the only ones.

Sofia needed a non-integer, and that's impossible for her to move because 1, 2, 3, 4, 5, and 6 are all integers.

So it's impossible that she'll get a non-integer.

And then Lucas needs a prime number.

Well, that's an even chance.

Remember, our prime numbers are 2, 3, and 5, and our non-primes are 1, 4, and 6.

So therefore, there's an even chance that Lucas will get a prime number.

Time now for the second part of our lesson.

And in this part, we're gonna be comparing the likelihood of events on the scale.

When there are multiple events that are likely to happen, one event can be more likely than another.

So what we've got down here is a scale of likelihood for spinners landing on win.

For the spinners we've now drawn on, they're all likely to land on win, but some are more likely than others.

Can you see what's happening as our spinners move from left to right? The sector for win is getting larger, which means it's becoming more and more likely that I'd win.

Similarly, when there are multiple events that are unlikely to happen, one event can still be more unlikely than another.

So here, we have almost the opposite happening in that the sector for losing is getting bigger and bigger and bigger as opposed to the sector for winning getting bigger and bigger, and that's because it's becoming less and less likely that I will win.

Laura and Sofia are playing a game that involves rolling a dice to determine if you can move your piece forward.

Laura can move her piece if she rolls a multiple of 3, and Sofia can move her piece if she rolls a multiple of 4.

For both players, their likelihood of moving is unlikely, but which way around would you put them on the scale? So, who's gonna be closer to impossible, and who is closer to the even chance? What do you think? Well, let's consider when Laura can move.

She can only move if she gets a multiple of 3, so there are two outcomes where this works for her.

What about Sofia? Well, for her, there is only one outcome that allows her to move.

This means that Sofia is more unlikely, or you could say less likely, to move than Laura is.

Note that the other outcomes for the dice roll are possible.

Aisha and Jacob are about to play each other in a tennis match.

The only possible outcomes are either Aisha wins or Jacob wins, so there's no drawing here.

Alex is considering where the likelihood of each person winning would go on our scale of likelihoods.

Do you think you can work out where they'd go at the moment? I agree, I think I need a bit more information to work out where each person would go.

Alex thinks that they both could be likely to win, but Aisha is more likely to win than Jacob.

Oh, okay, maybe Alex knows something about how good Aisha is at tennis.

So he's placed them here on the scale.

Now, I think Alex has to be incorrect based on where he's placed them.

So even though Aisha might be better at tennis, and maybe that's why he's done this, I still think they're not quite in the right place.

Why do you think that might be? Well, in this scenario, there are only two possible outcomes which cannot both happen in the same trial, which means that when one happens, it causes the other to not happen.

So the more likely it is that Aisha wins, the less likely it must be that Jacob will win.

So they can't both be likely to win because either one wins or the other wins.

So as you can see, as Aisha becomes more likely to win, Jacob becomes less likely to win.

And we can see them moving away, which makes sense.

For example, if Aisha was certain to win, then Jacob definitely cannot win.

So if Aisha's likelihood of winning was certain, then Jacob's likelihood of winning must be impossible.

Let's do a quick check.

Andeep, Laura, and Sofia are playing a game that involves rolling a dice to determine if you can move your piece forward.

Andeep can move his piece if he rolls a number less than 6.

Laura can move her piece if she rolls a factor of 6.

Sofia can move her piece if she rolls an odd number.

Which letter represents the likelihood that Andeep will move his piece? Pause the video and select the letter now.

Welcome back.

Which letter did you go for? You should have gone for C.

There are five numbers that are less than 6 on the dice and only one that isn't.

This means that it's very likely Andeep will move, but it's not certain.

Which letter do you think will represent the likelihood that Laura moves her piece? Remember, she can move her piece if she rolls a factor of 6.

Welcome back.

Which letter did you pick for Laura? That's right, it should have been B.

The factors of 6 are 1, 2, 3, and 6.

So there are four outcomes, and that's why it's likely, because there are four that allow her to move and only two that do not.

Remember, not as likely as Andeep moving 'cause there were five outcomes that worked for him.

A spinner contains only two outcomes.

So here, we've got the set of outcomes which involves win and lose.

The likelihood that the spinner lands on win is represented on the scale of likelihoods.

Can you see it? It's on the left-hand side, very near to where it says impossible, but not quite there.

So which letter do you think will represent the likelihood the spinner lands on lose? Pause the video and make your choice.

Which one did you go for? You should have picked D.

Remember, the more unlikely that we're going to win means the more likely we are that we're going to lose.

What about if the likelihood of me winning was here? So you can see it on the scale again.

Which letter would now represent the likelihood the spinner lands on lose? Pause and make your choice now.

Welcome back.

Did you pick C? Remember, as our likelihood of something happening moved on our scale, the likelihood of the other event happening moved as well.

So in other words, as something became more unlikely, the other event became more likely, and that's when we had our two outcomes.

Let's consider now our final task.

A game involves drawing a card from the deck below to determine who moves, and the information shows what a card needs to contain to allow each person to move.

What I'd like you to do, please, is represent the likelihood of each person moving their piece on the scale of likelihoods by writing the first letter of their name in the correct place.

Pause and do this now.

For question two, a set of spinners each only contain two possible outcomes, win or lose.

The likelihood for each spinner landing on win is shown on the scales below.

So for each scale, I'd like you, please, to mark the position that represents the likelihood of losing for each of these spinners.

Pause and do this now.

Welcome back.

Let's go through our answers.

So for question one, you had to write down the likelihood of each person moving their piece on the scale.

For Aisha, it is quite unlikely.

Remember, she has to get a vowel, and only A, E, and I are vowels here.

For Izzy, she has to get a consonant, and because it was unlikely that Aisha'd move, Izzy's is very likely.

So she's quite near to the end of the scale.

In fact, Aisha is as close to impossible as Izzy is to certain.

For Jacob, he wanted a prime number.

So it is quite unlikely, but if you look, there are more prime numbers in those cards than there were vowels.

So his chance of moving, or his likelihood of moving, is better than Aisha's.

Sofia wanted a factor of 24, and over half of the numbers on the cards are factors of 24.

So she's got a better than even chance, which makes it likely, but it's not quite as good as Izzy's.

And then Lucas wanted a square number, which is unlikely, and you should have placed Lucas in between Aisha and Jacob.

For question two, you had to mark down the position that represented the likelihood of losing on each spinner.

So for A, you should see that W is as close to certain as L is to impossible.

And then for B, the gap between W and even chance should be the same as the gap between the even chance and where L is on the unlikely side of the scale.

Again, that same mirroring effect around the even chance for C.

And then for D, if there's an even chance of winning, there has to be an even chance of losing.

Let's sum up what we've learned today.

The likelihood of events can be represented on a scale.

An impossible event has no possibility of happening, and a certain event is guaranteed to happen.

An event has an even chance if its likelihood of happening is the same as its likelihood of not happening.

Multiple events can be equally likely to happen without having an even chance.

And some events can be more likely to happen than others.

Well done.

You've worked really well today, and I hope you've enjoyed learning about the scale of likelihoods.

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