Possibility Diagrams for Two Dice
This animation builds a 6×6 grid showing all 36 ordered outcomes when two dice are rolled, treating (2,5) and (5,2) as distinct results. It labels each cell with its sum and, separately, its product, then highlights specific totals like sum 7 and product 6 to count favourable outcomes. Probabilities are calculated as fractions of 36, showing that while outcomes are equally likely, sums and products are not. Suitable for O Level, IGCSE and GCSE students studying probability diagrams.
Narrated · 16:9 · Preview before teaching · automatic layout checks do not establish subject accuracy
The prompt that made it
Explain Possibility Diagram for Two Dice for O Level students. Show all 36 outcomes, then find the sum and product of outcomes and use them to calculate simple probabilities. Keep it clear, visual, and engaging. Audience: O level, IGCSE, gcse, Edexcel students Teaching plan: Learning goal: Students will use a 6×6 possibility diagram to list all 36 equally likely ordered outcomes for two dice, calculate each outcome’s sum and product, and find simple probabilities from the diagram. 1. Introduce an outcome as an ordered pair (first die, second die). Build a 6×6 grid: rows and columns 1–6, showing all 36 outcomes, including (2,5) and (5,2) as different outcomes. 2. Annotate the grid with sums: add each pair’s values. Highlight patterns such as sum 7 and explain that probabilities come from favourable outcomes ÷ 36. 3. Model a sum example by counting the cells giving a chosen total, then calculate its probability. Emphasise that outcomes are equally likely, but sums are not equally likely. 4. Create a second grid or labels for products: multiply the two values in each cell. Highlight a product event, such as product 6, and count its favourable outcomes. 5. Work through product 6: identify the ordered pairs that produce it, count them, and write the probability as a fraction, simplifying when appropriate. 6. Check understanding: students locate outcomes matching a stated sum and product, count them, and explain why reversing the dice can create a separate outcome.
Make the next one in this series
- Show a possibility diagram for the difference between two dice scores
- Compare probability distributions of sums for two dice versus three dice
- Explain conditional probability using a two dice possibility diagram
