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I have a pile of coloured cards in a box containing 2 blue, 2 red and 2 yellow cards.

My experiment consists of taking two cards from the box with replacement.

I'm pretty sure the sample space is all possible combinations of two cards {BB, BR, BY,RR etc}.

What is the event space? Is it just one element i.e. BR, because the experiment consists only of taking two cards? Or does the event space ignore the amount of times the experiment is undertaken and is therefore the powerset?

I can't seem to find information on this anywhere.

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Here, the event space will be the set of all subsets of the sample space. In other words, it's the power set of $\Omega$, i.e. the sample space. The sigma-algebra of the experiment associates each subset of the sample space with a probability measure.

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