### Video Transcript

Probability: Certain, Possible,
Impossible

In this video, we’re going to learn
how to use the words “certain,” “possible,” and “impossible” to describe the
probability or the chance of different things happening.

To begin with, let’s go over our
three words, and these are words we use in everyday life all the time. If we say that something is
certain, we’re saying that it’s definitely going to happen. There’s no doubt about it. Sometimes, it’s hard to think of
things that are definite or certain. A good place to start though is
maths. There are lots of certainties in
maths.

For example, if we have a square
and we measure the angle of one of its corners, we know that we’re going to find
that it will measure 90 degrees or a right angle. It always will. This is one of the things we know
makes a square a square. It has four corners and they’re all
right angles. So we could say that it’s certain
that the angle inside the corner of a square will measure 90 degrees. And maths has lots of other
certainties too.

Now, it might be interesting if we
think about the word impossible next. And the reason is this is the
complete opposite to something being certain. We use the word impossible to
describe something that definitely won’t happen. It’s never going to happen. There’s no chance at all of it
happening. These are the examples that is
always quite fun to think of. If you press pause on the video for
a moment and peek underneath your chair, it’s impossible that you’re going to see a
snowboarding polar bear down there. There’s no chance of it
happening. It’s not even slightly possible,
which brings us onto our third word “possible.”

If certain is something that’s
definitely going to happen and impossible is something that’s definitely not going
to happen, then we can think of the word possible as living in between these two
opposites really. In maths, we use the word possible
to describe something that might happen. There’s some chance that it might
happen. We could say it’s possible that it
will rain tomorrow. We couldn’t say it was certain,
even if we lived in a really wet place. And we can’t say it’s impossible,
even if we lived in a really hot place. That would mean there was no chance
at all of it happening.

Instead, we say it’s possible. There’s a chance that it might
happen. Might not be very big chance, but
there’s a chance. Now that we’ve learned what these
three words mean, let’s have a look at some more examples and see whether we can say
whether they’re certain, possible, or impossible.

Is this event certain, possible, or
impossible? A goat will fly past the
window.

Now, it’s not very often in maths
that we get a question about flying goats, is it? But we’ve got one here, and it’s
all about probability. The chance of something
happening. And the event that this question is
talking about is the chance that a goat is going to fly past the window. Our question is asking us if we
were to get up from our computer now and look out of the window, what’s the chance
that if we look up to the sky, we’ll see a goat flying past?

Now, we could answer this question
in lots of different ways, but we’re given three different words to choose from. We need to answer using one of
them. Is this event certain? Is it possible or impossible? Let’s remind ourselves what these
three words mean. We use the word “certain” to
describe something that definitely will happen. There’s no doubt about it. There’s no chance at all of it not
happening. It’s certain. The opposite of certain is actually
our third word, “impossible.” If an event is impossible, it’s
definitely not going to happen. There’s no chance at all of it ever
happening. It’s absolutely impossible.

But then, in between these two
opposites, we’ve got the word “possible.” And we use this word for events
that could happen. They might happen. They might not, but there’s some
chance that they could. Now, which one of our three words
are we going to use to describe a goat flying past the window? Well, hopefully the idea of a goat
flying made you smile. It’s not possible at all, is
it? Goats don’t fly. We know it’s not certain, but it’s
also not even possible. There’s not the slightest chance
it’s going to happen; it’s impossible. We can say that the probability or
the chance that a goat will fly past the window can be described as impossible.

Is it possible, impossible, or
certain that someone watches television four times a week?

This question is all about the
likelihood of something happening. Is it possible that it will
happen? Is it completely impossible? Or is it absolutely certain? We can use these words to describe
the probability of something happening. And the event that this question is
talking about is someone watching television four times a week. Let’s have a think about our three
possible answers. If it’s certain that someone
watches television four times a week, then it’s always true that they watch
television four times every week, never any less, never anymore.

If we say that something’s
impossible, we’re saying that there’s no chance of it happening. It’s not even possible that someone
could watch television four times a week. And then we’ve got the word
“possible.” If a statement like this is
possible, then there’s a chance that it could happen. It might not happen, but there’s a
chance that it could. I wonder, how many times do you
watch television a week? Although some people might watch
television four times a week, we can’t say that it’s always true, can we? But we can’t say that it’s never
true, either. When something’s impossible,
there’s no chance of it happening.

Of course, there is some
possibility that someone could watch television four times a week. It’s quite easy to do really, isn’t
it? The only word we can really use to
describe this event is “possible.” It’s possible that someone watches
television four times a week, and it’s possible that they don’t. It’s a statement that’s sometimes
true. Maybe it’s true of you. Maybe it’s not. It’s possible that someone watches
television four times a week.

Now, so far in this video, we’ve
had to think about events that happen or don’t happen in the case of flying goats in
everyday life. And we looked at just one event
every time. What’s the probability of it
raining? What’s the chance of there being a
snowboarding polar bear? But, you know, sometimes we have to
apply some more maths than this. We could start using the words more
and less. Is something more likely to happen
than something else or less likely?

Let’s use this empty plate for a
taste test. And let’s imagine there are three
types of sweets. There’s the toffee twirl and the
strawberry supreme, both of which are delicious. But then we’ve got these
orange-colored sweets, coffee and carrot crunch. Let’s imagine that we really don’t
like the sound of these, and we want to avoid them as much as possible. But just to make things really
difficult, we’re going to do this taste test with our eyes covered up. Here it goes. Now thankfully, on the screen here,
we’ve got the benefit of being able to see the plate of sweets. What do you notice?

All of the sweets are that flavor
we don’t like, aren’t they? So if we were to come back to our
three words again, we could use the word “certain.” It’s certain that a coffee and
carrot crunch is going to be chosen. There’s no doubt about it. It’s definitely going to
happen. It doesn’t matter which sweet we
pick. We’re definitely going to have to
eat a coffee and carrot crunch. And because this is certain, we
could say that picking one of the other two flavors is actually impossible. There’s no chance of it
happening.

Now, let’s change our plate of
sweets. This is interesting. This time we’ve got five strawberry
supremes and two toffee twirls. And we have to say we’re very
grateful that there’s not a coffee and carrot crunch to be seen. So what can we say about the
possibility that we’re going to pick one of those horrible flavored sweets now. Well, there aren’t any to pick. So it doesn’t matter which sweet we
choose; we’re never ever going to have to taste the coffee and carrot crunch. It’s impossible.

But can we use the word “certain”
to describe anything this time? Well, I suppose we could say it’s
certain that we’re going to get a flavor that we like. But because there’s a mixture of
flavors this time, we can’t quite be sure which one we’re going to end up with. It’s possible that we’ll pick a
toffee twirl. But then there are some strawberry
supremes on the plate too. And it’s possible that we could
pick one of those. Can you see how we had used the
word possible here to describe the chance of us picking one of these two
flavors?

But you know, there’s something
else we could say about these sweets. And it comes back to what we were
saying a few moments ago about using the maths words more and less. If we look at this plate of sweets,
we can see that there are more red sweets than there are blue, can’t we? So if we were going to choose one
of these sweets at random — in other words, without seeing it, without planning what
we wanted to pick — we could say that it’s more likely that a red sweet is going to
be picked than a blue sweet. It’s possible that we’ll pick a
blue sweet, but it’s more likely that we’ll end up with a red sweet.

Even without seeing what we’re
doing as we put our hand on the plate, it’s more likely that we’re going to pick a
strawberry supreme. There are more of them. And of course, the opposite’s
true. It’s less likely that a blue sweet
is going to be chosen than a red sweet. But don’t forget, it’s even less
likely that we’re going to pick a coffee sweet. It’s impossible. So as well as thinking about
real-life events like we did earlier on, we can also use the words ”certain,”
”possible,” and ”impossible” in sort of experiments like this, where we pick things
randomly. Let’s have a go at answering a
question that’s a little bit like this sweet example. And it involves choosing something
else that we can’t see.

If there are three red balls and
nothing else in a bag, is it certain, possible, or impossible that if I pick out a
ball at random, it will be red?

This is quite a wordy question
really. So let’s go through it really
slowly to understand what it’s asking. Firstly, we’ve got a description
and that’s of three red balls and nothing else in a bag. Let’s sketch them. Here are our three balls. And let’s use this circle to
represent the bag that they’re in. Now, there’s a really important
part of that first phrase that we haven’t mentioned yet. And, it’s these two words here. We’re told that there are three red
balls and nothing else in the bag. There aren’t any other colors. There aren’t any other objects. Those three red balls are the only
things in that bag.

Now this question is all about
what’s gonna happen if we pick out a ball at random. When something like this happens at
random, it happens by chance, without any planning or decision-making. If we wanted to pick a ball at
random, maybe we’d close our eyes or, like in the example of this question, we put
the balls inside a bag where we can’t see them. This way, we can’t choose what we
pick. Now the color that we’re asked
about is red.

So this question is asking us,
what’s the chance that we’re going to pick a red ball? And we’re given three possible
answers. Is it certain that we pick a red
ball? Is it possible that we pick a red
ball? Or is it completely impossible that
we pick a red ball? We know that the word ”impossible”
means there’s no chance at all. It’s definitely not going to
happen. Now, if we put our hand into that
bag, we can’t say there’s no chance at all of us pulling out a red ball. We could say it’s impossible we’d
pick out a green ball. It’s impossible we’re going to pull
out a cheeseburger. But we can’t say it’s impossible
we’re going to pull out a red ball. The bag’s full of them.

Let’s get rid of this as a possible
answer. Speaking of possible, is it
possible that we pull out a red ball? We know that when something is
possible, there is a chance of it happening. It might happen; it could
happen. Now this word sounds like it could
be right. It is possible that we pull out a
red ball. But it’s time to come back to those
two words in that first phrase that we said were so important. There are three red balls and
nothing else in a bag. We wouldn’t use the word possible
to describe the chance of us pulling out a red ball. It’s much more than that. It’s absolutely certain because
there’s nothing else in that bag.

If we put our hand in, wiggle it
around, and pull out a ball, it’s going to be red, definitely. And if something is definitely
going to happen, we use the word ”certain.” If you’re not sure about this, try
it. If you don’t have colored balls,
then try three coins that are the same. As long as you don’t put anything
else in your bag, then you’ll see that the chance of you pulling out a red ball or
one of your coins is certain. If there are three red balls and
nothing else in a bag, the chance of us randomly picking out a ball and it being red
is certain.

So what have we learned in this
video? We’ve learned how to use the words
”certain,” “possible,” and “impossible” to describe the probability or chance of
something happening.