A sample space diagram is simply a diagram that helps you display outcomes in a logical and clear way. When two events take place, there are a number of possible outcomes.
Two dice are thrown and the results are shown in this sample space diagram.
What is the probability that the two dice will show different numbers?
The sample space diagram shows that there are 6 x 6 = 36 outcomes in total.
The ones showing doubles are shaded. There are 6 of these, and so 36 - 6 = 30 where the numbers are different.
P(different numbers) = 30/36 = 5/6