Introduction and key concepts
Probability is the study of the chances of things happening in future. We often make statements like “I am sure it will never happen”; “I have no chance of winning the prize!”, “I am sure it is going to snow this year.” Each of the statements tries to predict a future event.
In this chapter we will learn about:
- the probabilty scale and making predicitions.
- games of chance and fair and unfair games.
- the difference between an event and an outcome.
- tree diagrams and two-way tables.
- weather predictions.
The probability scale
To describe the probability that something will happen we can use a probability scale. This scale is a continuous line that starts with impossible events at the left-hand end and ends with certain events at the right-hand end. All probabilities must fall somewhere on this line. An event that is described as “impossible” is one that we know will never happen, such as having 8 days in one week. An event is described as “certain” if we know that it will definitely happen, such as having a Monday in a week. Between the two ends of the line are word descriptions: very unlikely, unlikely, even chance, likely, very likely.
We can also give numbers to the probabilities on this scale. Remember, though, that each word description covers a range of continuous probabilities on the scale, and it doesn't match a particular number exactly. The word descriptions used describe the mathematical meaning.
Example 1: Working with the probability scale
Give each of these events a word description from the probability scale.
- What are the chances of winning the Lottery if you buy a ticket every week for two months?
- How likely is it that you will pass Maths Literacy this year?
- What are the chances of rainfall in your area today?
- What are the chances of a pregnant woman having a male child?
- It is highly unlikely that a particular person will win the Lottery.
- Your answer here would depend on your personal situation.
- You can give your own answer, depending on the current weather and forecasts.
- A 50% (equal) chance.
Probabilities between 0 and 1 can be written as decimals, common fractions or percentages. So our probability scale could look like this:
Exercise 1: Becoming familiar with the probability scale
Work in a group to answer the following questions about the probability scale:
Discuss whether you think it is easier to describe a probability using a number or a word description.
Learner-dependent answer. Encourage learners to discuss the fact that will probably give different answers if they use words, while using a number ensures that everyone has the same understanding.