Video: Use the language of probability and the probability scale

﻿Hi, I'm Mrs. Dennett, and by the end of this lesson, it's likely that you'll be very good at using the language of probability, and almost certain that you'll be able to understand and interpret the probability scale. Here's a spinner divided into 10 equal sectors. We need to choose the word that best describes the likelihood of each event. An example of an event will be something like the spinner lands on red. Or another event could be the spinner lands on yellow. We also have a list of words that describe the likelihood of the event occurring. If we start with the spinner lands on red, we can see five out of 10 of the sectors on the spinner are red. That's half of the spinner. The other half isn't red, so there is an even chance that the spinner will land on red. What about yellow? Two sectors of the spinner are yellow. Eight aren't yellow, so it is unlikely that the spinner will land on yellow. It's less than an even chance. What about the probability or likelihood that the spinner lands on green? Only one sector is green, so it's unlikely. In fact, it's less likely than the spinner landing on yellow. The likelihood of a spinner landing on white. We don't have any white sectors, so this is impossible. The probability that the spinner lands on red, yellow, green, or blue, is certain. The spinner has to land on one of these colours, as these are the only ones that fill the spinner. Here's a question for you to try. Pause the video to complete the task, and restart when you are finished. Here are the answers. You can see that the spinner landing on an even number is unlikely. There are only two even numbers, four and eight, out of a total of eight sectors. The spinner landing on five is an even chance, because half of the sectors have a number five on them. The spinner landing on a number less than 10 is certain. All of the numbers on the spinner are less than 10. The probability that the spinner lands on a prime number is likely. The prime numbers on the spinner are three, five, and seven, and there are six opportunities for the spinner to land on one of these numbers. The spinner landing on a multiple of six is impossible. The multiples of six are six, 12, 18, and so on. There are no multiples of six on the spinner, so this is impossible. We're now going to look at some more events and consider the likelihood of them happening. What do you think is the likelihood of swimming 20 miles in 10 seconds? 20 miles is a very long way, and 10 seconds is quite a short period of time. So this event will be impossible. What about selecting a red sweet at random from a bag of six red and two yellow sweets? The probability of selecting a red sweet is likely, as there are more red sweets than yellow sweets in the bag. Next, let's consider throwing a fair dice and getting a one. Think about the numbers on a dice. They have one, two, three, four, five, and six. It's quite unlikely that we would get a one, as we could also get two, three, four, five, or six when we throw the dice. So, this event we say is unlikely. The next one to think about is flipping a fair coin and getting a head. We could get a head or a tail, so this one would be even chance. Lastly, taking one hour to walk three miles when walking at three miles per hour. If we walk at a constant speed of three miles per hour for one hour, then we will definitely walk three miles. This one is certain. We have a question for you to try. Pause the video to complete the task, and resume when you are finished. Here are the answers. It is true that you're unlikely to roll a one on a dice, as there are five other possibilities that you could get, namely two, three, four, five, or six. Although it's very unlikely that you will throw a coin and get a hundred heads, it is not quite impossible. It could happen, so this statement is false. In a pack of 52 playing cards, half of the cards are red and half of the cards are black, so there's an even chance of picking a red card. This statement is true. Here's another question for you to try. Pause the video to complete the task and restart when you are finished. Here are the answers. In this question, just because there are two outcomes doesn't mean that it's an even chance. Here, it depends upon how many raffle tickets are sold. And in a raffle, usually lots of tickets are sold. In this raffle, there is only one prize, so only one winning ticket, making it very unlikely that Jack will win. We have revised the language of probability. Let's check that we understand the probability scale. We start with an impossible event, an event that can't happen at all. If it's unlikely, it's further down the scale. Even chance is exactly in the middle of the probability scale. And likely is a little bit further to the right. And then we have certain at the other end. So, what is the probability that an event is impossible? If it's impossible, the probability is zero. What's the probability that an event is certain? If it's certain, definitely going to happen, we use one. One is also the same as 100%, so you may see 100% there too, representing the whole. What is the probability that an event has an even chance of occurring? We know this is halfway down the probability scale, so this will be 0.5. We could also write this as 50% or 1/2. When we write a probability, we can use a fraction, a decimal between zero and one, or a percentage. Let's have a look at the probability scale in action. Here's the spinner we looked at in our first example. It has 10 sections, so I'm going to split my probability scale up in the same way. So, it has 10 equal parts. To start, we want to know where to draw an arrow, to show the probability of the spinner landing on red. There are five red sections on my spinner, out of a possible 10 in total. 5/10 is the same as a half. So I need to put my arrow right in the centre of my probability scale. Yellow, I can see I have two sectors coloured yellow. This is 2/10. My arrow goes here. And then the probability of green, I have one sector coloured in green, so this is 1/10, and that arrow goes here. Here's a question for you to try. Pause the video to complete the task, and restart when you are finished. Here are the answers. For question four, we have to decide whether the statements are true or false. We can write probabilities as percentages, so 25% can be a probability. We must never write probabilities as ratios though, so the second statement is false. 1.2 is greater than one, so it cannot be a probability, so this statement is also false. For question five, we can see that the scale is split into four equal parts or quarters. So, 1/4, 2/4 are 1/2, and 3/4 are the missing fractions. Here's a final question for you to try. Pause the video to complete this task, and restart the video when you are finished. Here is the answer. We can see that there are 10 balls in the bag. Our scale is split into five equal parts, so each part represents two balls. We have two orange balls in the bag, so the arrow goes on the first marker. We say that 2/10 or 1/5 of the balls are orange. That's all for this lesson. Remember to take the exit quiz. Thank you for watching.

Worksheet: Use the language of probability and the probability scale

Exit Quiz: Use the language of probability and the probability scale

Lesson summary: Use the language of probability and the probability scale

Apply the vocabulary of probability to scenarios and label the probability scale with words and numbers.

Express Maths

Y11 Express Maths (Foundation)

Key Stage 4

Year 11

Use the language of probability and the probability scale

Probability 1 & 2

UNIT

Calculate probabilities from equally likely events

Find the probability of an event not happening including using a table (include mutually exclusive and exhaustive)

Find the predicted number of outcomes

List outcomes in a sample space diagram (two-way table) and calculate probabilities

Calculate experimental probabilities and make predictions (relative frequency)

Find probabilities from Venn diagrams including basic set notation

Find probabilities from frequency trees

Maths

Y11 Maths (Foundation)

Probability 1 (Scale and equally likely events)

Handling Data/Probability (D)

THEME

Use the language of probability and the probability scale - Exit Quiz

1.  Alice is labelling the probability scale. Can you spot her mistake? 

2. Alice is labelling the probability scale.Which phrases are missing?

3. There are 12 doughnuts in a box. Which letter represents selecting a donut with pink icing?

Express Maths

Use the language of probability and the probability scale

Video

Worksheet

Use the language of probability and the probability scale

Question 1

Question 2

Question 3

Q1.Alice is labelling the probability scale. Can you spot her mistake?

Q2.Alice is labelling the probability scale.Which phrases are missing?

Q3.There are 12 doughnuts in a box. Which letter represents selecting a donut with pink icing?

Use the language of probability and the probability scale

Question 1

Question 2

Question 3

Q1.Alice is labelling the probability scale. Can you spot her mistake?

Q2.Alice is labelling the probability scale.Which phrases are missing?

Q3.There are 12 doughnuts in a box. Which letter represents selecting a donut with pink icing?

Lesson summary: Use the language of probability and the probability scale

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