074. Probability Language and Simple Events
Learning Intentions
- To know the meaning of the terms experiment, trial, outcome, event and sample space
- To understand that the probability of an event is a number between
and inclusive representing the chance it will occur - Calculate probabilities of simple events
Pre-requisite Summary
- Understand that chance can be described in everyday language such as impossible, unlikely, even chance, likely and certain
- Be able to list possible results in simple chance situations such as tossing a coin or rolling a die
- Know that fractions can represent part of a whole
- Be able to count favourable outcomes and total outcomes
- Understand that a result can be recorded from one attempt or from many repeated attempts
- Know that a number line can be used to place values between
and - Understand that
means no chance and means certainty
Worked Examples
Worked Example 1
For a fair coin toss:
a) State the experiment
b) state one trial
c) list the sample space
d) Identify one outcome and one event
Worked Example 2
For rolling a fair six-sided die:
a) list the sample space
b) identify the event “rolling an even number”
c) Solve the probability of rolling an even number
Worked Example 3
A bag contains
a) list the possible outcomes by colour
b) find the probability of choosing a red counter
c) find the probability of choosing a blue counter
Worked Example 4
For spinning a fair spinner with equal sections labelled
a) identify the event “landing on a vowel”
b) find the probability of that event
c) place the probability on a scale from
Worked Example 5
A bag contains
a) find the probability of choosing yellow
b) find the probability of choosing green
c) state which event is more likely
Worked Example 6
For a fair die:
a) find the probability of rolling a number greater than
b) find the probability of rolling a number less than
c) Explain why one probability is close to
Problems
Problem 1
For a fair coin toss:
a) state the experiment
b) state one trial
c) list the sample space
d) identify one outcome and one event
Problem 2
For rolling a fair six-sided die:
a) list the sample space
b) identify the event “rolling an odd number”
c) find the probability of rolling an odd number
Problem 3
A bag contains
a) list the possible outcomes by colour
b) find the probability of choosing a red counter
c) find the probability of choosing a blue counter
Problem 4
For spinning a fair spinner with equal sections labelled
a) identify the event “landing on a vowel”
b) find the probability of that event
c) place the probability on a scale from
Problem 5
A bag contains
a) find the probability of choosing yellow
b) find the probability of choosing green
c) state which event is more likely
Problem 6
For a fair die:
a) find the probability of rolling a number greater than
b) find the probability of rolling a number less than
c) explain why one probability is small and the other is equal to
Exercises
Understanding and Fluency
Exercise 1.
Match each term with its meaning:
a) experiment
b) trial
c) outcome
Exercise 2.
Match each term with its meaning:
a) event
b) sample space
c) probability
Exercise 3.
For each chance situation, list the sample space:
a) tossing a fair coin
b) rolling a fair six-sided die
c) spinning a fair spinner with sections
Exercise 4.
Identify the event and favourable outcomes:
a) rolling an even number on a die
b) tossing a head on a coin
c) choosing a vowel from cards labelled
Exercise 5.
Calculate each probability:
a) head on a fair coin
b) rolling a
c) rolling an odd number on a fair die
Exercise 6.
Calculate each probability:
a) choosing a red counter from a bag with
b) choosing a blue counter from the same bag
c) choosing a colour that is not in the bag
Exercise 7.
A spinner has equal sections labelled
a) landing on
b) landing on an odd number
c) landing on a number greater than
Exercise 8.
A bag contains
a) green
b) yellow
c) not yellow
Exercise 9.
State whether each probability is impossible, unlikely, even chance, likely or certain:
a)
b)
c)
Exercise 10.
State whether each probability is impossible, unlikely, even chance, likely or certain:
a)
b)
c)
Reasoning
Exercise 11.
Explain why the probability of an event must be between
Exercise 12.
A student says the probability of rolling a
Exercise 13.
Explain why the sample space for a fair coin toss has two outcomes.
Exercise 14.
A student says the probability of rolling a number less than
Exercise 15.
Explain why an event with probability
Exercise 16.
A student says an outcome and an event are always the same thing. Explain why this is not always true.
Problem-solving
Exercise 17.
A bag contains
a) state the sample space by colour
b) find the probability of choosing a blue pen
c) state whether choosing a blue pen is unlikely, even chance, or likely
Exercise 18.
A fair spinner has equal sections labelled
a) find the probability of landing on a vowel
b) find the probability of landing on a consonant
c) state which event is more likely
Exercise 19.
A fair die is rolled once.
a) find the probability of rolling a factor of
b) find the probability of rolling a number greater than
c) compare the two probabilities
Exercise 20.
A box contains
a) find the probability of choosing green
b) find the probability of choosing red or green
c) state whether choosing white is likely or unlikely
Potential Misunderstandings
- Students may confuse an experiment with a trial
- Students may think an outcome and an event always mean exactly the same thing
- Students may list outcomes incorrectly when forming a sample space
- Students may count all outcomes incorrectly when calculating probability
- Students may forget that probability is a number from
to inclusive - Students may think a larger denominator always means a larger probability
- Students may Use the number of favourable outcomes as the probability without dividing by the total number of outcomes
- Students may think impossible events can have a small positive probability instead of