Handling Data · Chance or Probability · Lesson 1
How Likely Is It? Impossible, Possible and Certain Events
Every day we say things like 'It will probably rain' or 'There is no way I can finish that by noon'. In this lesson you will learn to describe how likely an event is using the words impossible, possible and certain, and to give examples from your own life.
By the end you will be able to
- ✔Describe an event as impossible, possible or certain.
- ✔Give examples of impossible, possible and certain events from personal contexts.
- ✔Use words such as unlikely, even chance and likely to compare possible events.
- ✔Place events on a probability scale from 0 to 1.
Key words
- Event
- Something that may happen, such as 'the coin lands heads' or 'it rains tomorrow'.
- Impossible
- An event that can never happen; its probability is 0.
- Possible
- An event that might or might not happen; its probability is between 0 and 1.
- Certain
- An event that will definitely happen; its probability is 1.
- Chance (probability)
- A number that tells how likely an event is to happen.
Curriculum reference
Content standard: B7.4.2.1 Identify the sample space for a probability experiment involving single events and express the probabilities of given events as fractions, decimals, percentages and/or ratios to solve problems.
Indicator: Demonstrate understanding of likelihood of a single outcome occurring by providing examples of events that are impossible, possible, or certain from personal contexts.
Starter
Will the Black Stars win?
Before every Black Stars match your uncle, your aunt and your neighbour all have an opinion: 'We will surely win!' 'No chance!' 'It could go either way.' Each person is judging how likely an outcome is. In mathematics we do the same, but carefully, with words and numbers that everyone understands in the same way.
1. Three important words: impossible, possible, certain
Some things can never happen. Some things always happen. Most things are in between. Mathematicians use three words to describe this:
| Word | Meaning | Example |
|---|---|---|
| Impossible | It can never happen | A dog will fly tomorrow. A school bus will turn into a cow. |
| Possible | It may or may not happen | Someone in your class will become a teacher. A coin lands heads. |
| Certain | It will definitely happen | Ghana will still be an African country tomorrow. The day after Monday will be Tuesday. |
Notice that it is the event that is described, and we decide by thinking about what is really able to happen. The word 'possible' does not mean 'it will happen'. It only means that it can happen and that it is not sure.
Let us test ourselves with four events: (A) a coin lands heads up, (B) the day after Monday will be Tuesday, (C) a new-born baby will be a girl, (D) it will rain in Winneba in the first week of January. A coin lands heads or tails, so (A) is possible. Tuesday always follows Monday, so (B) is certain. A baby may be a girl or a boy, so (C) is possible. January is in the dry season on the coast, so rain in Winneba is possible but very unlikely (D).
2. Possible events: unlikely, even chance and likely
There is a very big difference between 'it might rain in Accra in January' and 'it might rain in Accra in June'. Both are possible, but one is much more likely! To describe possible events better, we add more words.
▶ The scale moves from impossible on the left to certain on the right. The nearer to the right, the more likely the event.
| Word | Meaning | Example from Ghana |
|---|---|---|
| Unlikely | Less than a half chance | It will rain at Tamale in the middle of the dry season |
| Even chance | As likely as not | A fair coin lands on heads |
| Likely | More than a half chance | It will be hot in Accra at noon in February |
▶ Three of the four sectors are red, so landing on red is likely — but landing on blue is still possible.
3. Giving examples from your own life
The curriculum asks you to find examples of each kind of event from your personal contexts, which means things from your own life at home, at school and in your community. Here are some ideas to think about.
- Impossible: You will sleep in Kumasi and wake up in London a minute later. Your school will reopen on 31 February. You will draw a blue bead from a bag that has only red beads.
- Possible: You will get a mark above 80% in the next mathematics test. Your trotro will arrive on time. It will rain on your next market day.
- Certain: You will be one year older on your next birthday. A normal school week has five school days. If you drop a stone, it will fall down.
When you decide, ask yourself two questions. First: 'Is there any way this could happen?' If the answer is no, it is impossible. Second: 'Is there any way this could fail to happen?' If the answer is no, it is certain. If you answered yes to both questions, the event is possible.
4. Avoiding common mistakes
A good habit is to test your idea with an experiment. Toss a coin 20 times and record the heads and tails. Because heads and tails are equally likely, you expect about 10 of each, but not exactly 10. Try it in class with different groups and compare. You will see that results vary, which is exactly why we need words like 'possible' and 'likely' and not just 'will' or 'will not'.
In the next lessons you will learn to put numbers on these chances, using fractions, decimals, percentages and ratios.
Worked examples
Try each one yourself first, then open the solution and compare every step.
Example 1
Classify the event
Show the solution
- Step 1(a) A dog cannot fly: impossible.
- Step 2(b) Some learners may become teachers, but not sure: possible.
- Step 3(c) Ghana will always be in Africa: certain.
Answer: (a) impossible, (b) possible, (c) certain
Example 2
Coin, day and baby
Show the solution
- Step 1A: heads or tails can happen, so possible (even chance).
- Step 2B: Tuesday always follows Monday, so certain.
- Step 3C: a baby can be a girl or a boy, so possible (even chance).
Answer: A possible, B certain, C possible
Example 3
Rain in Winneba
Show the solution
- Step 1Can it happen? Yes, rain is sometimes recorded even in the dry season, so it is not impossible.
- Step 2Is it sure? No, most of the time it is dry in January.
- Step 3So it is possible, but unlikely.
Answer: Possible but unlikely
Example 4
Beads in a bag
Show the solution
- Step 1(a) There is no green bead, so it is impossible.
- Step 2(b) There are red beads, but also blue ones, so it is possible.
- Step 3(c) Every bead is red or blue, so it is certain.
Answer: (a) impossible, (b) possible, (c) certain
Example 5
Your own examples
Show the solution
- Step 1Impossible: I will walk from Cape Coast to Tamale in 5 minutes.
- Step 2Possible: I will score 70% or more in my next mathematics test.
- Step 3Certain: I will be older tomorrow than I am today.
Answer: Any three correct examples like these
Summary
- An impossible event can never happen (probability 0); a certain event will always happen (probability 1).
- A possible event may or may not happen; its chance lies between 0 and 1.
- Possible events can be described as unlikely, even chance or likely.
- Test an event by asking: could it happen? Could it fail to happen?
- Possible does not mean it will happen, and unlikely is not the same as impossible.
Practice: 15 questions
5 easy, 5 medium, 5 hard. Each one is marked straight away, with a full worked solution.
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