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A sample space is an important concept in probability, thus it is paramount that one understands the concept. A sample space is a set (see reference) of which each element in the set are an outcome of an experiment.
[ex.] A classic example of a sample space is that of a coin toss. In said case the sample space, which is denoted Ω = {H,T}. The {} brackets denote the set, as is conventional, and H refers to the outcome coin is heads, and T refers to the outcome coin is tails.
[ex.] Another solid example is the months of the year. In said case H={Jan,Feb,Mar,Apr,May,Jun,Jul,Aug,Sep,Oct,Nov,Dec}.
Note that the outcome of an experiment (i.e. what is outcome toss?) must fall in either of the states of Ω. In reality it may be possible for a toss to be neither, which tells us we may want to refine our definition of Ω.
As you may be able to imagine, sometimes we may be interested in two different things. Perhaps we may be interested in whether the day of the month is odd or even, and which month it is at the same time. For this we introduce the concept of events.
An event is a subset of the sample space (Ω).
[ex.] Lets use our month example again and define two events - which are sets - with one being the months of the year that have 31 days, and the other being the months of the year that have an R in the name
L={Jan,Mar,May,Jul,Aug,Oct,Dec} R={Jan,Feb,Mar,Apr,Sept,Oct,Nov,Dec}
We may then be interested in the intersection of these two sets. So that would be an event in L and R, denoted L∩R. This is not probability specific, but a set operation. this intersection is a new set, namely L∩R={Jan,Mar,Oct,Dec} (check!)
note: It may well be that L∩R. is an empty set. This means this is an impossible event. Take the Event=[meeting is in a long month] and Event={Sept,Nov}. In this case the intersection would be an empty set.