073r. Describing the Likelihood of Events

Learning Intentions

• To understand that we can describe the likelihood of events using phrases such as ‘even chance’, ‘unlikely’ and ‘certain’
• describe the likelihood of an event

Pre-requisite Summary

• Understand that an event is something that may or may not happen
• Be able to identify possible outcomes in a simple situation
• Know that some events happen more often than others
• Understand everyday words such as impossible, unlikely, even chance, likely and certain
• Be able to compare events as less likely, equally likely or more likely
• Recognise that likelihood can be described without calculating exact probabilities

Worked Examples

Worked Example 1

a) Explain the meaning of the terms impossible, unlikely, even chance, likely and certain.
b) Put these terms in order from least likely to most likely.

Worked Example 2

A fair coin is tossed.
a) Describe the likelihood of getting heads.
b) Describe the likelihood of getting tails.
c) Explain why these events have an even chance.

Worked Example 3

A bag contains $1$ red counter and $5$ blue counters.
a) Describe the likelihood of picking a red counter.
b) Describe the likelihood of picking a blue counter.
c) Explain which event is more likely.

Worked Example 4

A standard die is rolled.
a) Describe the likelihood of rolling a $7$.
b) Describe the likelihood of rolling a number less than $6$.
c) Describe the likelihood of rolling an even number.

Worked Example 5

A spinner has $4$ equal sections: $3$ are green and $1$ is yellow.
a) Describe the likelihood of landing on green.
b) Describe the likelihood of landing on yellow.
c) Explain why one event is likely and the other is unlikely.

Worked Example 6

For each event, describe the likelihood:
a) the sun rising tomorrow
b) choosing a letter A from the word CAT
c) choosing a vowel from the word DOG

Problems

Problem 1

a) Explain the meaning of the terms impossible, unlikely, even chance, likely and certain.
b) Put these terms in order from least likely to most likely.

Problem 2

A fair coin is tossed.
a) Describe the likelihood of getting heads.
b) Describe the likelihood of getting tails.
c) Explain why these events have an even chance.

Problem 3

A bag contains $2$ red counters and $6$ green counters.
a) Describe the likelihood of picking a red counter.
b) Describe the likelihood of picking a green counter.
c) Explain which event is more likely.

Problem 4

A standard die is rolled.
a) Describe the likelihood of rolling an $8$.
b) Describe the likelihood of rolling a number greater than $1$.
c) Describe the likelihood of rolling an odd number.

Problem 5

A spinner has $5$ equal sections: $4$ are blue and $1$ is orange.
a) Describe the likelihood of landing on blue.
b) Describe the likelihood of landing on orange.
c) Explain why one event is likely and the other is unlikely.

Problem 6

For each event, describe the likelihood:
a) it raining every day for the next year
b) choosing the letter E from the word BED
c) choosing a consonant from the word HAT

Exercises

Understanding and Fluency

1. State the likelihood word that best matches each description:
   a) will not happen
   b) has a $50\mathrm{\%}$ chance
   c) will definitely happen

2. Put these likelihood words in order from least likely to most likely:
   a) likely
   b) impossible
   c) certain
   d) unlikely
   e) even chance

3. Describe the likelihood of each event:
   a) rolling a $3$ on a fair die
   b) rolling a $9$ on a fair die
   c) rolling a number less than $7$ on a fair die

4. Describe the likelihood of each event:
   a) getting heads when flipping a fair coin
   b) getting tails when flipping a fair coin
   c) getting both heads and tails on one flip

5. A bag contains $1$ yellow counter and $7$ purple counters. Describe the likelihood of:
   a) picking yellow
   b) picking purple
   c) not picking purple

6. A bag contains $4$ red counters and $4$ blue counters. Describe the likelihood of:
   a) picking red
   b) picking blue
   c) picking either red or blue

7. A spinner has equal sections labelled A, A, B, C. Describe the likelihood of:
   a) landing on A
   b) landing on B
   c) not landing on C

8. Describe the likelihood of each everyday event:
   a) tomorrow coming after today
   b) a person having $3$ heads
   c) drawing a vowel from the word FISH

Reasoning

9. Explain why getting heads on a fair coin is an even chance.

10. A student says rolling a $6$ on a fair die is impossible. Explain the mistake.

11. Explain why an event can be unlikely without being impossible.

12. A student says that if an event is likely, it is certain. Explain why this is incorrect.

Problem-solving

13. A jar contains $9$ black marbles and $1$ white marble. Describe the likelihood of drawing a white marble and justify your answer.

14. A game uses a spinner with equal sections labelled sun, moon, moon, moon. Describe the likelihood of landing on moon.

15. A card is chosen from the letters in the word MATHS. Describe the likelihood of choosing a vowel.

16. A bag contains $5$ counters labelled $1,2,3,4,5$. Describe the likelihood of choosing a number greater than $3$.

17. A weather report says there is no chance of snow in Brisbane today. Which likelihood word best describes snow today?

18. A raffle ticket is drawn from a box with $100$ tickets, and you own $50$ tickets. Describe the likelihood of your ticket being drawn.

Potential Misunderstandings

• Students may think unlikely means impossible
• Students may think likely means certain
• Students may confuse even chance with likely
• Students may describe an event without considering all possible outcomes
• Students may use everyday language loosely rather than choosing the best likelihood word
• Students may think an event with one possible successful outcome is always unlikely, even when there are very few outcomes in total

Next: 074. Probability Language and Simple Events