Year 9 Maths • AC9M9P01 • Authored homework
Compound probability and tree diagrams
List all outcomes for compound events with and without replacement, use organised lists, tables and tree diagrams, and calculate probabilities by multiplying along branches and adding suitable outcomes. Show working, use correct probability language, and interpret answers in context.
Part A
Short-answer questions
List all outcomes when a coin is tossed and a six-sided die is rolled.
A spinner has red, blue and green. It is spun twice. How many ordered outcomes are possible?
What does “with replacement” mean in a probability experiment?
What does “without replacement” mean?
Why does probability change on the second draw when an item is not replaced?
Draw the first two levels of a tree diagram for tossing two coins.
In a tree diagram, what operation is usually used along a branch pathway?
A bag has 3 red and 2 blue counters. What is P(red on the first draw)?
Two fair coins are tossed. Find P(two heads).
Correct this error: “P(red then blue) = P(red) + P(blue).”
Part B
Long-answer questions
A bag contains 4 red and 6 blue counters. One counter is drawn, replaced, then another is drawn. Draw a tree diagram and find P(two red).
The same bag has no replacement after the first draw. Draw a tree diagram and find P(red then blue).
Compare the probability of drawing two red counters with replacement and without replacement. Explain why the answers differ.
A cafe offers 3 drink sizes and 4 flavours. Use a table or tree diagram to list all possible orders.
A student chooses one shirt from 5 shirts and one pair of shoes from 3 pairs. Use multiplication to find the number of possible outfits and explain the method.
A family has three children. List the possible birth-order outcomes for boy/girl and find P(exactly two girls).
A spinner numbered 1 to 4 is spun twice. Find the probability that the total is 5. Show the sample space.
Create a compound probability problem involving cards, counters or spinners and solve it using a tree diagram.
Explain when an organised list is enough and when a tree diagram is more useful.
Write a full worked response for a compound event, including sample space, tree diagram reasoning, probability calculation and interpretation.
Part C
Research and understanding task
Design a fair compound chance game using coins, dice, cards, counters or spinners. List the sample space, calculate at least two probabilities, and explain whether the game is fair.