Counting Events

The key to calculating the probability of an event is to count the number of ways the event can happen and then divide that by the total number of possible events. As an example, the graph below helps calculate the probabilities for events involving a pair of dice--a red one and a green one so that we can tell them apart.

To calculate a probability using the graph, click on each pair meeting a given condition. For example, to find the probability that the red face up matches the green face up (that is, [1,1], [2,2], [3,3], [4,4], [5,5], and [6,6]), click on the corresponding pairs in the graph below. As you click each pair, the probability is updated.

Click on a pair to add it to the probability calculation. Click on any highlighted pair to remove it from the probability calculation. Click on the Reset All button to remove all selections.

There are six different possible events for which the red face matches the green face. (You should have clicked on the diagonal pairs in the graph.) And there are thirty-six possible events in all. Thus, the probability that the red face will match the green face on any toss equals 6/36 = 1/6 = 0.167 or about 17 percent. Be sure to click on the Discovery button to try calculating a number of other probabilities.