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## Events

Events are certain subsets of the sample space; we will be able to define the probability of an event. For our purposes, we may think of any subset of the sample space as being an event. (In other situations, there are subsets of the sample space that can't be considered as events, and for which no probability can be defined.)
Example: For the experiment of tossing two coins, there are four possibilities in the sample space, since there are four outcomes: HH,HT,TH,TT. HH is the outcome of a head on the first and the second, HT is the outcome of getting a head on the first and tails for the second, TH is the outcome of getting a tail on the first and a heads on the second, and TT is the outcome of getting a tail on both. We think of each of these as being a single outcome of the experiment of tossing the coin twice. Remember that events are (in the examples we will look at) subsets of the sample space. Here are all the possible events for this setup: