Year 9 Maths • AC9M9P02 • Authored homework
Relative frequency, Venn diagrams and simulation
Calculate relative frequencies from data, use them to estimate probabilities, represent overlapping events with Venn diagrams, and compare simulations with theoretical expectations. Show working, use correct probability language, and interpret answers in context.
Part A
Short-answer questions
What is relative frequency?
A coin lands heads 27 times in 50 tosses. Find the relative frequency of heads.
How can relative frequency estimate probability?
Why can relative frequency change as more trials are added?
What does the overlap in a Venn diagram represent?
In a class of 30 students, 18 play sport and 12 play music. What extra information is needed to find how many do both?
What does P(A or B) mean in a Venn diagram context?
What does P(A and B) mean?
Give one advantage of using simulation in probability.
Correct this misconception: “Relative frequency must equal theoretical probability exactly.”
Part B
Long-answer questions
A student rolls a die 60 times and gets 14 sixes. Calculate the relative frequency of rolling a six and compare it to the theoretical probability.
A survey of 40 students shows 22 like maths, 18 like science and 10 like both. Draw or describe a Venn diagram and find how many like maths or science.
Use a two-way table or Venn diagram to represent students who play netball, soccer, both or neither. Explain each region.
Explain why a simulation with 20 trials may give a less stable estimate than a simulation with 2000 trials.
A spinner is believed to be unfair. Design an experiment using relative frequency to test the claim.
Compare theoretical probability, experimental probability and relative frequency using one example.
A weather app says there is a 30% chance of rain. Explain why it can rain tomorrow without the app being wrong.
Create a Venn diagram problem involving two overlapping events and solve for the probability of one combined event.
Use collected or invented data to calculate relative frequency and make a cautious prediction.
Write a full response explaining how Venn diagrams and relative frequency can work together to analyse a chance situation.
Part C
Research and understanding task
Collect or invent a small data set for a two-event situation, such as students’ hobbies, transport choices or app usage. Represent it with a Venn diagram and use relative frequency to estimate one probability.