Lesson video

Hi, I'm Mrs. Wheelhouse.

Welcome to today's lesson on non-equity likely Outcomes.

This lesson is in the unit probability possible outcomes.

I'm really looking forward to exploring probability with you today.

Let's get started.

By the end of today's lesson, you'll be able to state when outcomes will not be equally likely.

So just a quick reminder of some of the keywords we've looked at in previous lessons.

So they might be familiar to you, but if this is the first time you've seen them, don't worry.

They're on the screen now and you are very welcome to pause.

Have a read and maybe copy them down into your book if you think this is something that might be useful for you.

So feel free to pause now and just review these.

A new word for today is the word event, and an event is a subset of a sample space.

Now, what we mean by a subset is it contains some of the outcomes of that sample space.

Now it could be just one of them, it could be all of them.

So that's very possible.

So an event could be all the outcomes of a sample space or it could be just some of them.

There are two parts of today's lesson, and we're going to start with part one, which is identifying which outcome is more likely to happen.

Alex and Izzy are playing a game that involves spinning the spinner below to determine who gets to move forward.

Hmm, that's an interesting spinner.

I wonder who designed that.

Hmm.

I think you might be right.

I think it might have been Izzy because I think Alex is not very happy with this spinner.

Why do you think that might be? Alex says the spinner is more likely to land on Izzy's name than mine.

I have to say, Alex, I think you're right.

All right, Izzy adjust the spinner and says, well, how about this spinner? Does this now seem fair for both of us? So in other words, is it equally likely that the spinner will show Alex's name as it will land on Izzy's? What do you think? Alex says not quite.

The outcomes are still not equally likely to happen.

It's still more likely to land on your name than mine.

Can you see why? That's right, the sector for Izzy's name has a larger area than the sector for Alex's name.

Alex adjusts the spinner and says, well, how about this? I like this spinner.

I'm sure you do, Alex, but what do you think? Yeah, Izzy's spot on is still unfair.

The spinner is now more likely to stop on Alex's name rather than Izzy's.

To be fair though, I think Alex has a point.

It's not exactly like Izzy was making a fair spin and now was she? They decide that this will be their final spinner.

Alex thinks this seems fair for both of them, and Izzy points out that the two outcomes are now equally likely to happen, which means they both have an equally likely chance of winning their game because there's an equally likely chance that they'll be able to move each turn.

Remember, likelihood describes the chance that a particular event will occur.

For the spinner on the right, the sectors for Alex and Izzy are not the same size.

Therefore, the spinner is more likely to stop on Izzy's name than Alex's.

So the spinner on the left shows equally likely outcomes, whereas the spinner on the right shows an outcome that is more likely to happen than the other.

Now, we looked at this word event at the start of the lesson and we said that an event is a subset of sample space, so it could be one particular outcome or a set of outcomes that can happen when we perform a trial.

Jacob is going to spin this spinner once.

So that's our trial spinning the spinner once.

What we've got here is the set of all the possible outcomes.

So we could get an A, A, B, A, C, a, D, an E, an F, a G, or an H.

They are our individual outcomes and they make up our sample space.

Jacob points out that each of these outcomes is equally likely to happen, and that's because each outcome has its own sector and each sector is the same size.

He says, is the spinner more likely to stop on a vowel or a consonant? What do you think? What's your initial thought on this? Well, let's consider where the vows are in our sample space.

There are two possible vowels, A and E.

So the event that I get a vowel when I spin the spinner contains the two possible outcomes, A and E.

However, the event that I get a consonant on the other hand contains six possible outcomes, and that's B, C, D, F, G and H.

So our two events are either getting a vowel or a consonant.

There's the event I spin and get a vowel, and there's the event I spin and get a consonant.

I agree with Jacob.

The spinner is far more likely to land on a consonant than a vowel because there are more outcomes there.

And remember, each outcome individually was equally likely to happen.

Alex and Sophia are trying to decide who should get the last cookie in a jar.

Sounds good to me.

They decide to roll a regular six sided dice to term, who gets it.

Well, that's better than arguing about it.

Alex says if we roll a multiple of three, then you can have the cookie, and if it's not a multiple of three, I'll have it.

Who is more likely to get that cookie? Well done If you said, Alex, remember for Alex, there are four possible outcomes that allow him to have the cookie, and that's 1, 2, 4, and 5.

Whereas poor old Sophia, because she needs a multiple of three, only gets the cookie if it's a three or a six, still a quick check now, a counter is chosen at random from the bag and its letter is noted.

Now the counters are equal size.

So which statement is true? Statement A, the two outcomes are equally likely to happen.

B, the letter A is more likely to be picked than the letter B or option C, that the letter B is more likely to be picked than the letter A.

Pause the video while you make your choice.

Welcome back.

Which one did you go for? You should have gone for B.

Can you see that there are four counts in the bag that have an A on them and only three that have a B? Because our counts are all equal size, it doesn't mean we're going to choose one letter more than the other, but the fact there are more A's present than there are B's means it's more likely we'll pick A.

Another check now, which spinners have non-equally likely outcomes? Pause the video while you make your choice.

Welcome back.

Which ones did you go for? You should have picked A and C in A, it's more likely we'll pick lose than we will pick win.

And in C, it's more likely we'll pick win than we pick lose.

But in B, these outcomes are equally likely.

Time for your first task.

For each scenario, tick the outcome or event that is most likely to happen.

So in A, I'm rolling a regularly six sided dice, is it more likely I'll roll a multiple of two or that I'll roll a multiple of three for B, I'm going to spin that spinner once.

Is it more likely it will land on a factor of eight or more likely it will land on a factor of 12? In C, I'm going to pick a counter from the bag.

Is it more likely I'll pick A or more likely I'll pick B.

And then in D, I'm going to choose a letter at random from the word mathematics.

Is it more likely I'll choose a vowel or that I'll choose a consonant? Pause the video while you make your choices.

Welcome back.

Question two, starting with the least likely sort the spins in order of their likelihood of landing on win.

So remember, you are starting with the least likely for winning, which means most likely for losing.

Pause the video and do this now.

Welcome back time to go through our answers.

So for each scenario asked you to take the outcome or event that was most likely to happen.

So in one A, you are more likely to roll a multiple of two than you are to roll a multiple of three.

The only multiples of three on a regular six-sided dice are three and six.

So there's two, but rolling multiple of two could be two, four or six.

So there were three outcomes there.

In B, I said, what's more likely you'll land on a factor of eight or a factor of 12 and you should have chosen a factor of 12.

The factors of eight are one, two, four, and eight.

So there were four possible outcomes, but the factors of 12 are one, two, three, four, and six.

So there were five possible outcomes there.

So that was more likely.

In C, I said, which one's more likely and you should have chosen B, 'cause there are four counters showing B and only three showing A.

And then for D, what was more likely? And that's choosing our consonant.

There are definitely more consonants there than there are vowels.

In question two, I said to start with the least likely spinner for winning.

So you had to reorder these and the order should be D and then B, A, E, G, C, and F.

If I was going to play a game where I had to spin this spinner and I wanted to win, F would definitely be the spinner I would want to be playing with.

It's now time for the second part of our lesson.

I'm going to be recognising non-equally likely outcomes in context.

Laura and Aisha are going to play each other in a tennis match.

Jacob and Sam are considering the likelihood of the possible outcomes.

So remember either Aisha could win or Laura could win.

Jacob says, I think the two outcomes are equally likely because either Aisha wins or Laura wins.

I can see that reasoning, Jacob.

Oh, Sam thinks that one of these outcomes could be more likely to happen than the other.

I wonder why Sam thinks that.

Do you think that as well? So who do you agree with? Jacob or Sam? Pause the video while you discuss this.

Welcome back.

Let's have a think about this.

Laura says, I've never played tennis before.

Ah, Aisha's plays tennis every weekend and she's won lots of competitions.

Ah, okay, that's quite useful information.

Do we think it's equally likely that Laura will win and I shall win, or do we think it's more likely one of them is going to win rather than the other? What do you think? Yeah, Jacob's changed his mind and to be honest, so have I.

I think that Aisha is more likely to win than Laura.

I am with you, Jacob, because bear in mind Aisha wins loads of competitions.

So yeah, not equally likely there.

Andeep and Jun are thinking about whether it might rain tomorrow.

Okay, well either it's going to rain or not rain makes sense.

There are two outcomes.

Andeep says, well I think these outcomes are equally likely to happen because it either rains or it doesn't seems sensible, Andeep.

Jun says, I think one of these outcomes could be more likely than the other, depending on other factors.

Oh, who do you agree with? Andeep or Jun? Well, now the likelihood of an outcome could depend on the location.

So where we are based.

So in Spain it might be more likely that it does not rain a particular day than it does rain.

So for example, Madeira summer.

But in the UK it might be more likely that it does rain on a particular day.

I don't know what the weather's doing where you are right now, but actually if I look out my window, it is currently raining.

The likelihood of an outcome could also depend on the time.

So what do we mean by that? According to the Met Office data, the average rainfall in Bradford is the lowest in April and highest in December.

Hmm.

So depending on what month it is, it might be more likely to rain than not rain.

Spot on Jun, time of year could indeed be a factor.

The likelihood of two particular outcomes can be compared even when there are other outcomes that are possible.

So which weather is more likely to happen in the UK in December that we are more likely to get snow or a heat wave? Well now these are not the only two possible outcomes for weather events because it could rain, the temperature could be so so.

But these particular outcomes can still be compared to conclude that snow is more likely than a heat wave in December.

So it doesn't matter.

There are other possible outcomes just between these two we can decide which one's more likely.

So quick check which weather is more likely to happen in the UK in July? Are we more likely to have snow or a heat wave? Pause and make your choice.

Welcome back.

Did you pick a heat wave as well? So did I.

Now true or false, a novice swimmer races against a professional swimmer, it is equally likely that each person wins? So you think that's true or false? And then you need to justify your answer by selecting either A or B.

Pause and do this now.

Welcome back.

I'm hoping you picked false and that you justified it by selecting B.

The professional swimmer is more likely to win than the novice swimmer.

I certainly know if it was me, I think of myself as a novice swimmer racing against an Olympian swimmer, I should hope that they're going to win.

Otherwise I should change career and become an Olympic swimmer.

It's now time for your final task.

And in here, question one, we're asking for each context, tick the outcome that seems most likely to happen.

So for each row you have a context and then two possible outcomes.

Select the outcome that is most likely to happen.

Pause and do this now.

Welcome back.

Question two.

For each scenario, write down a contextual factor which might affect the likelihood of the outcomes.

So for example, if we consider the weather that we did before, we talked about, for example, time of year, we talked about which country we're in, their example of contextual factors.

So for each of the scenarios you can see A, B, and C.

Write down a contextual factor that might affect the likelihood of these outcomes.

Pause and do this now.

Welcome back.

It's time to go through our answers.

So for question one I said tick the outcome that seems most likely to happen.

So for a day in July in the UK it's more likely we had a heat wave, for a day in December in the UK though, it's more likely we'll have frost, a day in December in Australia.

Now if you don't know what the weather's like in Australia in December, you could of course looked this up.

You could have asked your family, friends, et cetera, used the internet, used a book.

But you should have discovered that a day in December in Australia it's a heat wave is most likely.

You may have even heard stories about having Christmas dinner on the beach, a drink stool in the UK in December.

Is it more likely that most customers will buy ice smoothies or that they'll buy hot chocolates? Well, if it's in December, it's probably more likely that we're buying hot chocolate.

A professional darts player in a running race against a professional sprinter.

Which outcomes more likely? Yeah, the professional sprinter is more likely to win.

And then what about if our professional darts player and our professional sprinter now have a darts match? That's right.

The professional darts player is more likely to win.

Question two.

Now for each scenario, write down a contextual factor.

So let's see what we've come up with.

So for A, Sam and Alex are playing each other in a chess match.

Well what might affect that is the experience of each player at playing chess.

So you might have said, for example, Alex is a chess whiz and Sam's never played before, means the same thing even though different ways of writing it.

B, Laura's predicting the weather and whether it will snow on a particular day.

So she said either snows or not snows.

There are two possible outcomes.

What might affect that or the time of the year.

You could have said location, the weather on the days leading up to it.

Lots of different options there and obviously you may have come up with another one that works too.

And then for C, Jun is buying an ice cream and choosing a flavour, well I think that's very likely to be affected by which flavours Jun prefers.

For example, he might hate mint, he might think vanilla is boring.

He might think chocolate doesn't taste quite right, lots of reasons why those outcomes may not be equally likely.

All right, it's time to sum up our lesson today, we've been considering non-equally likely outcomes.

It's important to remember that not all outcomes for trial are equally likely to happen.

And outcomes that are not equally likely to can be compared to determine which one is more likely to happen than the other.

Determining which outcome is more likely to happen can be affected by contextual factors.

And we saw examples like that in particular with the weather.

So for example, time of year, location, what the weather's been like in the days leading up to the day we are considering are all factors that could affect how likely a particular outcome is.

Well done.

You've worked really well today and I'm really pleased with how much you've been able to do.

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