Let’s suppose that:
- $60\%$ of students who study Chinese are artistic and love poetry.
- $20\%$ of students who study Business are artistic and love poetry, and
- Only about $1\%$ of students study Chinese, whereas about $15\%$ of students study Business.
Thus, out of every $1000$ students, there are $10$ studying Chinese, of whom $6$ are artistic and love poetry, and also there are $150$ studying Business, of whom $30$ are artistic and love poetry.
So if a student is artistic and loves poetry, it’s $5$ times more likely she’s studying Business than Chinese.
So much for preconceptions (and “correlation”).
