The Probability Scale
Impossible
0
Unlikely
Even Chance
0.5 or 1/2
Likely
Certain
1
Calculating Probability
The probability of an event is calculated with this formula:
P(event) = Number of favourable outcomes / Total number of possible outcomes
For example, the probability of rolling a 4 on a standard six-sided die is 1/6, because there is one '4' and six possible outcomes in total.
Probability Practice 🎲
1. A bag contains 5 red marbles, 3 blue marbles, and 2 green marbles.
a) What is the probability of pulling out a blue marble?
b) What is the probability of pulling out a red marble?
c) Is it more likely to pull a red or a blue marble?
2. You spin a spinner with 8 equal sections numbered 1-8.
a) What is the probability of landing on an even number?
b) What is the probability of landing on a number greater than 5?
3. Mark the following events on the probability scale below.
A) You will have homework this week.
B) A coin flip will land on heads.
C) It will snow in Auckland in July.
📚 NZ Curriculum Alignment
Mathematics & Statistics
Achievement Objective: S4-1
Plan and conduct investigations using the statistical enquiry cycle
Key Competencies
- • Thinking critically about probability concepts
- • Using mathematical language and symbols
📋 Teacher Planning Snapshot
Ngā Whāinga Ako — Learning Intentions
Students will engage with this resource to develop statistical investigation skills — planning inquiries, collecting and analysing data, interpreting distributions, and communicating findings. Tūhuratanga (investigation) is framed as a tool for understanding our communities and environment in Aotearoa New Zealand.
Ngā Paearu Angitū — Success Criteria
- ✅ Students can identify an investigative question, collect relevant data, and display it clearly.
- ✅ Students can interpret statistical findings and discuss what they might mean for a real-world community or environmental context.
Differentiation & Inclusion
Scaffold support: Provide structured investigation frameworks (PPDAC cycle templates) for entry-level access. Offer partially completed data tables for students who need additional support. Extend capable learners by asking them to critique a statistical claim from a news article, or to design their own community data investigation.
ELL / ESOL: Pre-teach statistical vocabulary (median, mode, range, distribution, sample, population). Pair visual representations (graphs, tables) with plain-language explanations. Allow students to discuss statistical ideas orally before writing. Encourage use of home language for initial sensemaking.
Inclusion: Statistical investigation offers natural differentiation — all students can engage with the same real-world question at different levels of mathematical complexity. Neurodiverse learners benefit from structured, step-by-step investigation processes. Use collaborative group investigation formats that distribute roles (data collector, recorder, analyst, presenter).
Mātauranga Māori lens: Tūhuratanga — the practice of careful investigation — resonates deeply with mātauranga Māori. The maramataka is a sophisticated data system: tracking environmental patterns, seasonal cycles, and ecological indicators over generations. Iwi environmental monitoring — counting kaimoana populations, tracking water quality, observing bird migrations — is applied statistical thinking. Framing statistics within community and environmental inquiry connects data to mana whenua responsibilities.
Prior knowledge: Students should have basic familiarity with data displays (bar graphs, dot plots). No prior statistical investigation experience required — the PPDAC inquiry cycle provides accessible scaffolding for first-time investigators.
Curriculum alignment
- Statistics — Statistical Investigation: Plan and conduct investigations using the statistical enquiry cycle — determining appropriate variables and data collection methods; gathering, sorting, and displaying multivariate category, measurement, and time-series data to detect patterns, variations, relationships, and trends; comparing distributions visually; communicating findings, using appropriate display.
- Statistics — Probability: Investigate situations that involve elements of chance by comparing experimental distributions with expectations from models of the possible outcomes, acknowledging uncertainty.