AC9M9P01Year 9ProbabilityPractised on site

AC9M9P01 — Year 9 Probability

Official Curriculum Content Description:

list all outcomes for compound events both with and without replacement, using lists, tree diagrams, tables or arrays; assign probabilities to outcomes

Worked Examples (2)

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Example 1Sample Space & Combined Events

A bag of marbles at the school fete contains 2 red marbles and 3 blue marbles. Two marbles are drawn one after another WITHOUT replacement (the first marble is NOT returned to the bag). What is the probability that BOTH marbles are red? Express your answer as a fraction in its lowest terms.

Common mistake: Keeping the same first-level probabilities on the second draw instead of adjusting for without replacement.

Correct Answer:

1/10

Worked Solution:

First draw

P(\text{red}) = \frac{2}{5}

. Since the draw is WITHOUT replacement, there are

1

red marbles left out of

4

total marbles. Second draw

P(\text{red} \mid \text{red}) = \frac{1}{4}

. Multiply along the branches:

P(\text{both red}) = \frac{2}{5} \times \frac{1}{4} = \frac{2}{20}

. Simplified:

\frac{1}{10}

Example 2Product Rule for Counting Outcomes

The school canteen offers a lunch deal with 7 choices of wrap or sandwich, 3 snacks, 5 pieces of fruit and 4 drinks. How many different 4-item lunch deals can a student choose, taking one item from each group?

Common mistake: Adding the number of options at each stage (

7 + 3 + 5 + 4 = 19

) instead of multiplying them.

Correct Answer:

420

Worked Solution:

By the product rule for counting, multiply the number of options at each stage:

7 \times 3 \times 5 \times 4 = 420

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