Probability

Lesson

An experiment or trial are the words used to describe the event or action of doing something and recording results. For example, the act of drawing cards from a deck, tossing a coin, rolling a dice, watching the weather, asking questions in a survey or counting cars in a carpark could all be examples of experiments or trials.

Some experiments are small, meaning the event is only repeated a small number of times (e.g. we may flip a coin 10 times). Here is a small experiment for you to try.

Objectives:

- To determine what makes a spinner fair.
- To compare theoretical probability and experimental probability.

Materials: cardboard, coloured pencils/ textas, sharp lead pencil.

Procedure:

1. Cut out a square of cardboard and colour it in so there's an equal chance of the spinner landing on red, yellow, blue and green. Then stick your lead pencil through the centre.

Question: What is the theoretical probability of a spinner landing on each colour?

2. Create a table like the one below. You can draw it or make a table on your computer.

Colour | Tally | Frequency |
---|---|---|

Red | ||

Yellow | ||

Blue | ||

Green |

3. Spin your spinner $20$20 times by twisting the pencil. Record the colour the spinner falls on in the table.

Questions: What was the experimental probability of landing on each question? Is this different to the theoretical probability?

Group task: Compare your results with the rest of the class and complete a frequency table with everyone's data (you can use a calculator to work out the frequencies if you like).

Questions: Was one colour more common that the others? Were the frequencies more or less even than your individual results? How could you change your spinners to make the experiment biased?

Some experiments are large, meaning the event is repeated a large number of times (e.g. we may flip a coin 100 times). Some experiments may involve hundreds or even thousands of trials! Here is a larger experiment for you to try.

Objective: to determine the modal sum of two dice.

This means that we're asking what number will be the most common (modal) number when we add the scores of the two dice together.

Materials: two dice (labelled 1-6), Race to Win leaderboard (below)

Procedure:

1. Split the class up into groups of three. Each group should choose a number between 0 and 12 which they think will be the most common sum of the dice. Each group **must **pick a different number.

2. Groups take turns rolling the two dice, adding the scores together and recording the answers on the leaderboard.

3. The first group to fill their column on the leader board wins.

Questions:

1. Why are some numbers more likely to be rolled than others? Draw a table on the computer like the one below. What patterns do you notice in their sums?

+ | 1 | 2 | 3 | 4 | 5 | 6 |
---|---|---|---|---|---|---|

1 | ||||||

2 | ||||||

3 | ||||||

4 | ||||||

5 | ||||||

6 |

2. Use your table to help you create a table of the theoretical probabilities. Remember, probability can be expressed as a fraction in the form:

$\frac{\text{Number of chances of rolling a particular number}}{\text{Total number of outcomes}}$Number of chances of rolling a particular numberTotal number of outcomes

3. How could this game be changed to make the chances of winning more fair?