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Prediction

Games of chance

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Probability games, for example using coins and dice, help us to understand probability better. These games work with random events, so they are a useful way to learn how to use probabilities to predict events.

Definition 1: Frequency
The number of times that something happens.
Definition 2: Random
When something happens without being made to happen on purpose.
Definition 3: Trial
A test. Throwing a dice or tossing a coin are examples of a trial.
Definition 4: Fair
Treated equally, without having an advantage or disadvantage.

Random events and equal chances

Two important points make games of chance useful for learning about probability:

First, the events in probability experiments are random. This means that they cannot be deliberately influenced in any way (provided that the game is fair!). There is no way of making a fair dice fall on one number rather than another.

Second, each possible outcome has an equal chance of occurring. All the numbers on a dice have exactly the same chance of coming up when the dice is tossed: i.e a 1 in 6 chance.

Because of these two facts, we know that when we toss a coin, we have a 50% or 0,5 or \(\frac{\text{1}}{\text{2}}\) chance of getting heads, and a 50% or 0,5 or \(\frac{\text{1}}{\text{2}}\) chance of getting tails.

Similarly, on a dice, there is a 1 in 6 chance of throwing a 1; 2; 3; 4; 5 or 6.

This chance is called the theoretical probability.

Definition 5: Theoretical probability
The calculated probability, not the actual result.

When you do a probability experiment, such as tossing a coin a number of times, you find the relative frequency of each outcome. For example, if you toss a coin 10 times and you get Heads 3 times, then the relative frequency is simply 3 in 10 or \(\frac{\text{3}}{\text{10}}\).

The difference between an event and an outcome

An outcome is the result of a single trial. For example, if I roll a dice, one outcome would be a 6. An event is a collection of one or more outcomes. Using the example of rolling a dice, an event might be rolling an even number. Thus this event consists of any of the outcomes 2; 4; 6.

Exercise 1: Experimenting with games of chance

    Exercise 2: More games of chance

    Figure 1: Dice with eight sides
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    Most dice are cubes, which means that they have six identical faces. It is also possible to get dice with different numbers of faces. As long as all of the faces are the same shape and size, the dice should still be fair.

    The photograph above shows some dice with 8 faces.

    1. List the possible outcomes when throwing one of these dice.

    2. What are the theoretical chances of throwing a “7” on one of these dice?

    3. Is it more likely that you will get an even number on these dice than on normal 6-sided dice? Explain.

    1. 1; 2; 3; 4; 5; 6; 7; 8

    2. 1 in 8 or 12,5% or 0,125

    3. The chance is the same, as there are the same number of even numbers and odd numbers on each type of dice.

    Work in two groups to carry out a new probability experiment. Colour in some paper disks red and blue. One group should make 8 red disks and 4 blue disks. The other should make 4 red disks and 4 blue disks.

    1. Put the disks into a closed box or bag and take turns to draw a disk out and note down which it is. (Remember to put the disk back each time.)

    2. Draw up a table and record your results.

    3. Write a few sentences to describe the difference in the two groups' results.

    1. Learner-dependent answer

    2. Learner-dependent answer.

    3. Learner-dependent answer.