# A student is artistic and loves poetry. Is it more likely she’s studying Chinese or Business?

Let’s suppose that:

1. $60\%$ of students who study Chinese are artistic and love poetry.
2. $20\%$ of students who study Business are artistic and love poetry, and
3. 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”).

### One Response to “A student is artistic and loves poetry. Is it more likely she’s studying Chinese or Business?”

1. Colin Beveridge

More starkly:

40% of Spice Girls are called Melanie.
0.2% of English-speaking girls are called Melanie (roughly).

But if you bump into someone called Melanie in the street, the odds are pretty good that she’s not a Spice Girl.