# One table, several questions

**Part B · L07 · 5–10 minutes · Prerequisite: L06**

## The situation and question

Keep the **D&D 2014 ordinary ability check** from L06, with a total bonus of +5.
How often would it meet DC 10, 15, or 20? These are three alternative difficulty
settings, not three successive checks or three opponents.

## Predict

Should the three probabilities add to 100%? A total of 20 meets *all three*
thresholds. The questions overlap, so there is no reason for their sum to be one.

## Build

Square brackets make a **list**: an ordered collection of values. Here, each
value is a labelled pair. Parentheses around `("Meet DC 10", chance)` group the
label and its probability into a two-item **tuple**. A comma separates the
items; commas also separate the rows. Tuples keep the two parts of a row together.

`prob_table(rows)` turns that list into one probability table. `output` still
presents the result. Every row's second item must be a probability between 0 and
1—not a mean, count, or percentage multiplied by 100. The table formats it for you.

```dice
bonus = 5
check = d(20) + bonus
rows = [
    ("Meet DC 10", check.p_ge(10)),
    ("Meet DC 15", check.p_ge(15)),
    ("Meet DC 20", check.p_ge(20)),
]
output("One ability check, alternative difficulties", prob_table(rows))
```

## Run and read

The rows should be **80%, 55%, and 30%**. For DC 10, natural faces 5–20
succeed: sixteen of twenty. The other counts are eleven and six of twenty.
Their sum is 165%, which is fine: they are separate, overlapping questions,
not exclusive outcomes. Do not multiply them to infer a chance of meeting all
three with one roll. On that same roll, meeting DC 20 already meets the others.

## Change one thing

Add a fourth row for DC 25 inside the list. Keep its label consistent with its
query. **Check:** the new row is 5%, one natural face out of twenty.

## Try it yourself

Build a two-row table for a single unmodified d6: “Exactly six” and “Four or
more.” **Answer check:** `.pmf(6)` gives 1/6 and `.p_ge(4)` gives 1/2. These
also overlap. You have assembled a report from a question, not simulated rolls.

## What you now know

A list of labelled probability questions makes a compact comparison. A report
must say whether rows are categories, alternative settings, or overlapping events.

## Rules and model notes

[D&D Basic Rules 2014, Using Ability Scores](https://www.dndbeyond.com/sources/dnd/basic-rules-2014/using-ability-scores),
**Ability Checks** and **Typical Difficulty Classes**, checked 2026-09-15.
Same scope as L06: one ordinary check, fixed total bonus, no attack exceptions,
advantage, rerolls, or special features. A harder DC changes the query, not the die.

## Where next

[Previous: averages and chances](06-averages-and-chances.html) · [Next: a loop](08-comparison-loops.html).
The [ordinary ability-check recipe](../cookbook/dnd2014-ability-check.html)
uses tables to keep related questions in one report.