# what is the difference between event space and probability space?

Let the sample space, $S=\{1,2,3,4\}$ and event space,$F$ is defined on $S$ are $\{1\}$ and $\{2\}$.Enumerate all possible events in $F$.

This is the question I encountered while solving problems on probability. Am I right that the answer could be $\{\varnothing,\{1\},\{2\},\{1,2\}\}$? Is my understanding about event space right?

• Do you think {null set,{1},{2},{1,2}} is a sigma-algebra on S={1,2,3,4}? – Did Jan 25 '15 at 8:50
• I think sigma algebra on s={} also includes possibilities of {3}{4}{3,4}{1,3}etc. Did they? – hello world Jan 25 '15 at 9:01
• It seems to me that you are in great need of definitions. Are you aware of the definition of a sigma-algebra? – Did Jan 25 '15 at 10:07

## 1 Answer

For your question in the title (which is different from the one inside) a way to view is,a grocery store: events correspond to packed items for sale (they may not sell a single apple, for example). Probability space corresponds to these packed items ALONG with their price.

• could you please elaborate further with an example? – hello world Jan 25 '15 at 9:39
• Event space corresponds to which subsets events. (Not every subset need be in it). This collection of events should for a sigma algebra. Probability space consists of this event space, along with a specification of probability for each event. – P Vanchinathan Jan 25 '15 at 10:04