Likelihood booklet
Likelihood booklet
- Unit 1: Numbers
- Unit 2: Geometry and measure
- Unit 3 : Statistics and probability
🎯 In this topic you will
- Use likelihood words to describe the chance of events happening
- Use experiments to investigate the chance of events happening
🧠 Key Words
- certain
- even chance
- good chance
- likely
- likelihood
- maybe
- no chance
- outcome
- poor chance
Show Definitions
- certain: An event that will definitely happen.
- even chance: An event that is just as likely to happen as not happen.
- good chance: An event that is more likely to happen than not.
- likely: Describes an event that has a high chance of happening.
- likelihood: How likely an event is to occur.
- maybe: Used when it is uncertain whether an event will happen.
- no chance: An event that cannot happen.
- outcome: The result of a single event or experiment.
- poor chance: An event that is unlikely to happen.
What Is Likelihood?
Likelihood is about how likely something is to happen. Many people need to know which event is most likely to happen or what the chance is that something will happen.
Why Likelihood Matters
Farmers and gardeners need to understand the likelihood of rainfall and sunshine so they can decide which crops to grow. Leaders also need to think about likely outcomes, because this helps them make better decisions.
❓ EXERCISES
$1.$ Choose one of these words or phrases to describe the likelihood that each event happens.
a. The sun will go down today.
b. I will drop a cake and it will fly upwards.
c. I will find a four-leaf clover.
d. I will be taller in three months.
e. I will pick a red apple from this bag without looking.
👀 Show answer
a. Certain
b. No chance
c. Poor chance
d. Good chance
e. Even chance
$2.$ Write an event of your own that matches the likelihood.
a. It is certain I will …
b. There is no chance I will …
c. There is a poor chance I will …
d. There is a good chance I will …
e. Maybe I will …
f. It is likely that I will …
👀 Show answer
a. I will breathe today.
b. I will turn invisible.
c. I will win the lottery.
d. I will finish my homework tonight.
e. I will see my friend tomorrow.
f. I will go to school this week.
$3.$ A website shows a head or tailon a coin when you press 'Flip the coin'.
Otto flips a coin $20$ times.
Copy and complete the table.
👀 Show answer
Heads: $11$
Tails: $9$
$4.$ Sal makes a spinner.
a. Chance of red?
b. Chance of yellow?
c. Chance of a colour?
👀 Show answer
a. $\dfrac{1}{3}$
b. $0$
c. $1$
$5.$ Jess spins a spinner $50$ times. Describe what it looks like.
👀 Show answer
Blue is the largest section.
Red and purple are equal-sized.
Yellow is slightly smaller.
There is no green section.
🧠 Think like a Mathematician
Roll a dice $50$ times and investigate the results. Draw a table to record how many times each number appears.
Your table could look like this:
| Number | Tally | Total |
|---|---|---|
| $1$ | ||
| $2$ | ||
| $3$ | ||
| $4$ | ||
| $5$ | ||
| $6$ |
Before rolling the dice, think about the questions below. Make a conjecture and then test it using your results.
- What do you think the tally chart will look like when you have finished? Why?
- How many $1$s do you think you will roll? Why?
- How many $6$s do you think you will roll? Why?
Roll the dice $50$ times and record the outcomes in your table. Answer the questions below using words such as likely, maybe, no chance, poor chance, even chance, good chance, or certain.
a. What is the chance of rolling a $3$?
b. What is the chance of rolling a $7$?
c. What is the chance of rolling an odd number?
d. What is the chance of rolling a number less than $10$?
Based on your investigation, write one conjecture of your own about chance.
👀 Show example answers
- a. There is an even chance of rolling a $3$.
- b. There is no chance of rolling a $7$ on a standard die.
- c. There is an even chance of rolling an odd number.
- d. It is certain that the number rolled is less than $10$.
- Conjecture: When a fair die is rolled many times, each number appears roughly the same number of times.
💡 Quick Math Tip
Fair dice outcomes: When a die is fair and rolled many times, each number from $1$ to $6$ is expected to appear roughly the same number of times, even though the results may not be exactly equal.