Part A: Numeracy
8

Probability

Evaluate risk, chance, and probability tree branches easily

Learning Objectives

  • ✓ Represent probability as fractions, decimals, and percentages
  • ✓ Analyse outcomes for independent and dependent events
  • ✓ Construct and solve problems using tree diagrams
  • ✓ Calculate expected value in real-world scenarios
Chapter Progress: 0%

Section 1: Language of Probability and Chance

Probability describes how likely an event is to happen. It ranges from 0 (impossible) to 1 (certain). Outcomes are the possible results of an experiment.

Section 2: Simple Probability Calculations

The formula for calculating simple probability is: P(Event) = Favourable Outcomes / Total Possible Outcomes.

Probability Formulas

Example 1

ACER Authentic Problem: Complementary Probability (July 2017 Q19)

❓ Question: A school sports day is scheduled for Friday. The Weather Bureau forecasts a 20% chance of rain on Friday. What is the chance that it will NOT rain on the school sports day?
📄 Source Passage / Reference Data:

CHANCE OF RAIN

Forecast: 20% chance of precipitation.

📝 Step-by-Step Method:
1
Identify the complementary event rule: P(not Rain) = 100% - P(Rain).
2
Express 80% as a fraction with denominator 100.
3
Divide numerator and denominator by 20 to reduce to lowest terms.
🔍 Evidence Extracted: "100% - 20% = 80% = 4/5"
🎯 Final Answer: 4/5
💡 Why It Is Correct: The probability that it will not rain is the complement of the probability of rain: 1 - 0.20 = 0.80 = 4/5.
⚡ LANTITE Exam Strategy: Official ACER Tip: Always check whether the question asks for the event or its complement ("not rain").

Section 3: Multi-stage Events and Tree Diagrams

For multiple events, tree diagrams help map out all possible outcomes. Multiply probabilities along the branches to find the probability of a combined outcome.

Example 2

ACER Authentic Problem: Venn Diagram & Non-Participation (July 2017 Q8–9)

❓ Question: Sixty students were asked which sports they play (football, basketball, both, neither). How many students reported that they DO NOT play basketball?
📄 Source Passage / Reference Data:

BALL SPORTS VENN DIAGRAM

Total cohort = 60 students.

STUDENT SPORTS PARTICIPATION (Venn Diagram)

17 Football Basketball 20 8 15
📝 Step-by-Step Method:
1
Count all students inside the Basketball circle (both + basketball only).
2
Subtract the basketball participants from the universe (60 students).
3
Alternatively, sum the regions strictly outside the basketball circle (Football only + Neither).
🔍 Evidence Extracted: "20 + 17 = 37 students outside basketball circle."
🎯 Final Answer: 37 students
💡 Why It Is Correct: The students who do not play basketball comprise those who play football only (20) plus those who play neither sport (17), giving 37 students in total.
⚡ LANTITE Exam Strategy: LANTITE Venn Strategy: "Do not play X" includes the "Neither" group outside both circles!
Question 1 of 10

ACER 2017 Q19: The Bureau forecasts a 20% chance of rain. What is the fraction chance that it will NOT rain?