VectorPaint two-dice sum maps: distinguish thirty-six outcomes from eleven totals

English translation of the Chinese original, translated on 2026-11-13. Original publication dates, attribution, code and version notes are retained.

Make a static probability teaching diagram, not a gambling activity or prediction of actual rolls. Two fair independent six-sided dice have 36 equally likely ordered outcomes when red/blue identities are fixed; totals 2 through 12 are not eleven equally probable outcomes. VectorPaint presents the distinction without performing random trials or automatic probability calculations.

Declare fairness, independence and die identities

Use a square canvas with blue-die columns 1–6 and red-die rows 1–6. Following the equally likely sample-space condition in the OpenStax probability chapter, state fairness and independence in the title. If conditions change, cell counts divided by 36 no longer transfer automatically. This is a paper model, not a claim of 36 observed rolls. Separate border, coordinates, sums, shading and audit marks; headers are not outcome cells.

Build all thirty-six cells rather than half a triangle

Arrange six equal rows and columns with external headers. Red 2/blue 5 and red 5/blue 2 both sum to 7 but are distinct ordered outcomes; retain both halves of the grid. Count six cells in each of six rows, excluding header corners. After copying, check for narrow duplicate strips from overlapping borders and preserve square proportions when scaling. Adjust text or canvas rather than deleting repeated sums, which would remove valid outcomes.

Read row and column before entering a total

Row one totals are 2,3,4,5,6,7; row two 3,4,5,6,7,8; row six 7,8,9,10,11,12. Identify red/blue values before adding, with small coordinate labels retained in an audit copy if desired. Red 1/blue 6 and red 6/blue 1 both give 7; red 6/blue 6 gives 12. Repeated adjacent totals suggest unchanged copied text. Preserve outcome identity separately from the sum so colour alone does not erase which pair generated a cell.

Shade the five ordered pairs summing to six

Use a light colour for sum 6 and list pairs (1,5),(2,4),(3,3),(4,2),(5,1): five cells. Red 6 has no blue 0 because faces run from 1 to 6. Locate from the list before shading; this is an anti-diagonal segment, not the main diagonal. Under the declared model its probability is 5/36. Label the colour “sum 6”, not “sum 5” from the cell count. Put audit dots on a separate layer so they do not resemble die pips.

Check six sum-seven cells and their union

Shade sum 7 separately at (1,6),(2,5),(3,4),(4,3),(5,2),(6,1): six cells and probability 6/36=1/6. No cell sums to both 6 and 7, so their union has 11 cells and probability 11/36, not (6+7)/36. Label the events mutually exclusive; adjacent colours share no outcome. Count 25 unshaded cells as another check: 11+25=36. A continuous-looking colour band is not a new die face.

Do not assign equal weights to the eleven sums

Counts for sums 2 through 12 are 1,2,3,4,5,6,5,4,3,2,1, totalling 36. Sum 2 has only (1,1) while 7 has six cases, disproving equal weights of 1/11. Doubles occupy six main-diagonal cells; sum 6 intersects them only at (3,3), while sum 7 has no such intersection. Diagonal appearance does not make events identical. Count cells rather than relying on gradients, and do not present theoretical probabilities as guaranteed next-roll frequencies.

Troubleshoot removed symmetric cells and misplaced legends

A total of 21 suggests deletion of exchanged red/blue outcomes. Six sum-six cells suggest an added zero or stray fill. Resolve text/colour conflicts through row-plus-column arithmetic, not by relabelling the event to fit a mistake. Inspect PNG headers enlarged for clipping and colours reduced for legibility, adding letters if colour alone is insufficient. Keep calculation and diagram traceable. Without running trials, report no empirical agreement; retain the editable source for another person’s cell audit.

Reopen and audit outcomes, events and sums

Save, leave and reopen. Audit 36 red/blue outcomes first, then five and six event cells, their eleven-cell union and the count sequence for eleven sums. Preserve fairness/independence in the title and distinguish totals from trial counts. Hide or explain audit marks, open output and record text, boundaries and colours without promising untested formats. Another reader should identify every outcome and explain repeated sums with unequal weights; no real-dice simulation or prediction is claimed.