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Or, for the second problem or correlations:

Do you have a Y chromosome? a) Yes b) No

Do you have two X chromosomes: a) Yes b) No

Each are 50-50 questions, but the answer to A is correlated to the answer to B.

It's hard to find questions whose answers are independent variables.

Perhaps not correlated in the way you are think, due to confounding factors:

A) how many people don't understand the questions

B) how many people understand the questions but don't choose to answer "correctly" e.g. transgender. E.g. smart arse Yes, Yes answers.

C) correlation with a third variable e.g. sampling bias (HN readers that answer internet surveys).