Before you can really begin to understand probability questions, there are a few words/phrases that you should be comfortable with. Let’s take a closer look!
When working with probability, we call anything that we can get a result from a probability experiment. You could consider rolling a die, flipping a coin, or randomly choosing a number a probability experiment. Depending on your perspective, you could even call driving to work a probability experiment with the possible results being you arrive on time or you don’t.
A single result of a probability is called an outcome (some books use the word “simple event”). When flipping a coin, the possible results or outcomes are heads or tails. In the example about driving to work, the outcomes are “on time” and “not on time”. As you can see, in some cases the perspective matters. Consider another example: rolling two six sided dice. We could look at the sum of the faces (if two sixes com up, then the outcome is 12) or just the faces themselves (6,6). Both of these could be considered outcomes.
The sample space for a probability experiment is the set of all possible outcomes. This is usually written with set notation (curly brackets). For example, going back to a regular 6-sided die the sample space would be:
The concept of a sample space is very important and so I’ve actually put together an article with more examples here: What is a sample space?
An event is any group of outcomes from the sample space. If I was flipping two coins, one event is that I get tails at least once. This happens with the outcomes (heads,tails), (tails, heads), and (tails, tails). Events can also be written using set notation. Looking at the event we just talked about, the event of “tails at least once” could be called E and written as .
Note that simple events involve only one outcome, for example rolling a 2 on a die. Using set notation: .
Now when you study a probability question, you can start to apply this terminology to better understand the question being asked and the situation overall. In many cases, finding the probability of an event only involves finding the number of outcomes in the event and the number of outcomes in the sample space (though sometimes that is much harder to do than you would think!).