In probability theory, at times, it becomes really tough to find the sample space as there are a lot of events involved. The use of tree diagram is not only in probability theory but also in making decision trees, game trees and event trees. The tree diagram will have branches where each branch is labelled with the probability of the event represented by the adjacent leave. The AND and OR operations can be easily represented using a tree diagram. As the branching is done and probabilities are written over there, the calculation for probability seems to be more convenient.

What is a Tree-Diagram

Tree diagram is a tree structure to represent a sequence. The tree diagram finds its use in probability theory, decision making and many other analytical applications. In probability theory, the tree diagrams are used to know the sample space of an experiment having more than one events. If there are two events happening simultaneously such as rolling a dice and tossing a coin then the sample space can be easily known using a tree diagram.

Tree Diagram with AND

The term AND stands for multiplication. For example, if a coin is tossed and a dice is rolled and we need to see the event where a head and a 6 will come in the rolling of dice are the examples of an AND event. In an AND event, the probabilities of events involved in multiplied. Now, in the tree diagram the first branching is to get a head and not to get a head. Then the second branching will be to get a 6 and not to get a 6.
Tree Diagram with AND

Tree Diagram with OR

The term OR stands for addition. If an event is defined in a way that a head will come when a coin is tossed or a 5 will come in rolling a dice then it is an example of an OR event. For an OR event the probabilities of all the included events is added. In the tree diagram, first branching will show about the first event and the second branching about the other event.
Tree Diagram with OR

Picturing Probabilities

In a tree diagram the probability of each event can be written on the branch before the event. A group of three members has to be formed from a class. Show the probability that all three are males. In the tree diagram we can show like this.
Picturing Probabilities