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I am a little unsure what the difference between Event spaces and Sample Spaces.

For exmaple, if you rolled a dice twice, what would be the sample space, and what would be the event space?

blademan9999
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1 Answers1

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Your two-trial probability experiment has sample space $\{11,12,13,14,15,16,21,22,\ldots,65,66\},$ which is the set of all its $(36)$ possible outcomes.

An event is a subset of the sample space; so, your probability experiment has $2^{36}$ possible events, including the empty set (i.e., an impossible event, e.g., ‘landing “$87$”’), the sample space itself (i.e., a certain event, e.g., ‘scoring a sum greater than $0$’), and any combination of the $36$ outcomes (e.g., $\{11,22,33,44,55,66\}=$ ‘landing the same number twice’).

Your probability experiment's event space is the set of all its $(2^{36})$ possible events.

I wrote more here.

ryang
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