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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 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.

    Reply

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