[ajsfoux234]

The PDF linked to in the post: https://web.archive.org/web/20181123120243/www.insidemathema... (the original link is dead)

Also, I wonder if posting a photo of the work with pencil annotations violates the CC NoDerivatives license.

[qsort]

Problem E of that set is hilariously wrong:

    The probability of being born a male is 0.466. The probability of being born in North America is 0.153846. The probability of being born in an urban location is 0.3571428. Find the exact probability that a baby will be born a male, in North America, in an urban location.

They obviously expect you to multiply those numbers (seven digit numbers with the quadratic algorithm -- poor kids), but the joint probability equals the product if and only if the random variables are independent, which in this case they are not.

Problem B (mentioned in the article) is probably not as bad as it looks: you can eyeball that the target sum is approximately half of the total, and you can probably match the final digit.

[OJFord]

These things are marked by humans, and appealable (in the case of exams, if it's just homework who cares) - IME in the UK, if you write something like 'insufficient information in the question, given RVs are not independent' then you are not going to be marked down for it; if they find the question incorrect it'll likely be struck off entirely.

But more likely, everyone answers either wrong (not because they know better) or right, because they don't know to do anything but multiply them; at the stage this is a question they don't know there are dependent and independent RVs.

It's like if you draw something that looks near enough a square and show it to someone in primary school, asking for the angle in the corners. The correct answer is 90 degrees, it doesn't matter that it's not exactly drawn, that we didn't define a coordinate system or the units we wanted.

[will4274]

Eh. My teacher just wrote "assume all probabilities are independent" at the top of the test.

Using only independent examples is a good way to have a lot of very repetitive problems where you take marbles out of bags of marbles.