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One green ball, one blue ball, and two red balls are placed in a bowl. I draw two balls simultaneously from the bowl and announce that at least one of them is red.

What is the chance that the other ball I have drawn out is also red?

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Two unit vectors in two-dimensional space \(\hat{\textbf{a}}\) and \(\hat{\textbf{b}}\) are added together. The expected magnitude of the resulting vector \(\textbf{a+b}\) is equal to \(E.\) What is \(\lfloor100E\rfloor?\)

###### Image credit: Wikipedia P.Fraundorf

Also try Daniel Liu's Expected Distance on a Circle.

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Five couples like to go to the movies together; they always sit in a row of ten adjacent seats. To shake things up a bit, they have a rule that nobody is allowed to sit next to their partner. How many seating arrangements are there for this party?

I thought of this problem while watching a bad (Hollywood) movie on a bad date ;)

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How many non-degenerate triangles can be formed with these dots?

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