


In order to discuss the notion of probability in more detail, we need to introduce some terminology. First, note that the word random is often used to describe an activity where the outcome is uncertain. In the urn example of Part 1, we would say that we are selecting a ball "at random" because we do not know the outcome of this activity.
We will discuss the probability of various outcomes in the context of a welldefined activity or procedure. We use the term experiment for such a welldefined procedure. An example is the procedure of selecting a single ball out of the urn. When an experiment is performed, the result is called an outcome. In our urn experiment, the possible outcomes are A green ball is selected and A red ball is selected. We also need a term for the set of all possible outcomes. We will call this set the sample space. So in our urn example, the sample space is a set consisting of the two outcomes.
Example: Rolling a die. Consider the experiment of rolling a single die. There are six possible outcomes: one of the numbers 1, 2, 3, 4, 5, and 6. So, in this case, the sample space has 6 elements. Assuming that we have a fair die (that is, each side is equally likely to turn up), we assign the probability of each outcome to be the ratio 1/6.
Example: Using a game spinner. Consider the experiment of spinning the pointer on the game spinner pictured below. There are three possible outcomes, that is, when the pointer stops it must point to one of the three colors. (We rule out the possibility of landing on the border between two colors.) Since the red region covers half the area of the spinner, we say that the probability of it pointing to the red area is 1/2. Similarly the probabilites of it pointing to the blue and green areas are 1/3 and 1/6 respectively.
Events
Not only do we want to assign probabilities to individual outcomes, but also we want to assign probabilities to sets of outcomes, i.e., to subsets of the sample space. A subset of the sample space will be called an event. So, how should we assign probabilities to events?
The following applet will allow you to experiment with rolling a pair of dice. Close the applet window when you are done.



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