Every probability question about two things at once — a PR’s size and whether it shipped a bug, a patient’s test result and their disease status — can be answered from one table of counts.
Your team audited the last 200 pull requests, classifying each by size and by whether it later turned out to have introduced a bug:
| bug | no bug | total | |
|---|---|---|---|
| small | 12 | 108 | 120 |
| large | 24 | 56 | 80 |
| total | 36 | 164 | 200 |
Three kinds of question you can ask this table (using probability-speak for “fraction of PRs”):
- Joint — both things at once: P(large and bug) = 24/200 = 0.12.
- Marginal — one thing, ignoring the other: P(bug) = 36/200 = 0.18. (“Marginal” because it reads off the table’s margins — the totals row/column.)
- Conditional — one thing, within the world where the other is true: P(bug given large), written P(bug | large). You throw away every row that isn’t “large” and ask the question inside what’s left.
Compute P(bug | large). While you’re in there, work out P(large | bug) too — you’ll want to notice whether it’s the same number.