Chance
🎯 In this topic you will
- Use precise probability language to describe chance events.
- Conduct chance experiments and clearly present and interpret the results.
🧠 Key Words
- chance
- likely
- might happen
- will happen
- will not happen
Show Definitions
- chance: The possibility that a particular event will occur during an experiment or situation.
- likely: Describes an event that has a high probability of happening.
- might happen: Indicates that an event is possible but not certain to occur.
- will happen: Describes an event that is certain to occur under the given conditions.
- will not happen: Describes an event that is impossible under the given conditions.
Making Better Decisions with Probability
Knowing about chance and probability helps you make better decisions. When you understand how likely something is to happen, you can judge whether it is worth trying or not.
Using Chance to Evaluate Choices
If you know something about chance, you can decide more confidently whether an action is likely to succeed or fail, helping you choose what to do next.
❓ EXERCISES
$1.$ You have six dominoes in a bag.
a. What is the chance that if you take out two dominoes, the total number of spots is more than eight? Draw a ring around the answer.
It will happen.
It might happen.
It won’t happen.
b. Is it likely that you will make a total number of spots that is less than eight? Explain your answer.
👀 Show answer
a. The correct choice is It might happen, because some pairs of dominoes have a total greater than $8$, but not all pairs do.
b. Yes, it is likely, because many combinations of two dominoes add to a total less than $8$, making this outcome more common.
$2.$ You will need a pencil and a paper clip for each spinner. Spin both spinners.
🧠 Reasoning Tip
To spin the spinner, put the paper clip in the centre of the spinner. Use the pencil to hold it in place while you spin the paper clip.
Add the two numbers. Do this $15$ times.
a. What totals do you think are likely to happen?
b. What totals do you think are not likely to happen?
c. Keep a chart of the totals. Write in all the possibilities.
d. Write about what happened.
👀 Show answer
a. Totals such as $4$, $5$, and $6$ are likely to happen.
b. Totals such as $2$ and $6$ may be less likely, depending on spinner outcomes.
c. Possible totals range from $2$ to $6$.
d. Results should show some totals appearing more often than others.
$3.$ You need one counter and one coin.
a. Put the counter in the middle of the crocodile.
b. Toss the coin. If you get heads, move one space towards the head.
c. If you get tails, move one space towards the end of the tail.
d. After ten tosses, where do you finish?
If you play the game again, will the same thing happen, will it not happen or might it happen? Give reasons for your choice. Play the game again and find out. What happened?
👀 Show answer
The finishing position can change each time because the coin tosses are random.
The correct description is that it might happen again, but it is not guaranteed.
🧠 Think like a Mathematician
Play this game.
You will need a paper clip and a pencil for the spinner.
Out of $24$ spins, which colour do you think will happen, will not happen or might happen? Write your predictions.
Method:
- Spin the spinner $24$ times.
- Record each result using tally marks.
- Complete the table with your estimates and actual results.
- Compare the outcomes with your original predictions.
| Colour | Will/Won’t/Might happen | Estimate how many times | Actual number of times, as a tally |
|---|---|---|---|
| green | |||
| blue | |||
| red | |||
| yellow | |||
| purple | |||
| orange |
Write about your results and compare them with your estimates.
Show Answers
- Colours with larger sections on the spinner are more likely to happen more often.
- Colours with smaller sections may still occur but less frequently.
- The actual tallies will vary, but after many spins they should roughly match the size of each coloured section.
- Results may differ from predictions because each spin is random.