## Sample Space?

Sequences, counting (including probability), logic and truth tables, algorithms, number theory, set theory, etc.
maroonblazer
Posts: 51
Joined: Thu Aug 12, 2010 11:16 am
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### Sample Space?

Hi,
I'm brushing up on my probability skills and the text asks the following question:
For the sample space {A, B, C, D}, determine how many events are possible.
I understand that an event is a subset of a sample space, so the question is essentially asking "how many subsets of {A, B, C, D} are there?"

Other than the brute force method of listing all the different subsets I can't figure out how to crack this question.

The book's answer is 16.

Help?
mb

maggiemagnet
Posts: 358
Joined: Mon Dec 08, 2008 12:32 am
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### Re: Sample Space?

If the answer is "16", then yes, they mean "all subsets"; in other words, all possible events (or outcomes), including combinations. So they don't just want "A, B, C, or D", but also "A and B", "A and C", etc.

They should have given you a formula for that. With a sample space of "n" elements (things int he set), there are 2n possible events.