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

Calculating Theoretical Probability of Selecting Classroom Resources

❓ Question: What is the probability of randomly selecting a red whiteboard marker from a teacher supply box containing 4 red, 3 blue, and 5 green markers?
📄 Source Passage / Reference Data: Whiteboard Marker Supply Box Inventory: 4 Red markers, 3 Blue markers, and 5 Green markers.
📝 Step-by-Step Method:
1
Calculate the total number of possible outcomes by summing all markers.
2
Identify the number of favourable outcomes (red markers).
3
Apply the probability formula: P(Red) = Favourable outcomes ÷ Total outcomes.
4
Simplify the fraction by dividing numerator and denominator by 4.
🔍 Evidence Extracted: "4 Red markers out of 12 total markers"
🎯 Final Answer: 1/3 (or 33.3%)
💡 Why It Is Correct: There are 4 red markers out of 12 total markers. Dividing 4 by 12 and simplifying yields 1/3.
⚡ LANTITE Exam Strategy: In LANTITE probability questions, simplify your final fraction by dividing numerator and denominator by their greatest common factor.

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.

Section 4: Using Tables and Venn Diagrams to find Probabilities

Two-way tables and Venn diagrams organize data for overlapping categories, making it easier to calculate probabilities involving "and" and "or".

Question 1 of 6

What is the probability of rolling a 3 on a standard six-sided die?