Tree Diagram and the Fundamental Counting Principle
Tree diagrams show the different possible outcomes of a series of events where they are organized as they occur. Probability outcomes obtained must sum up to a whole number, 1 depicting all outcomes have been considered. On the other hand, the fundamental counting principle, the counting rule, helps figure out the number of outcomes in a probability situation. Primarily, one multiplies the events of the case together in which he would thus obtain the total number of outcomes. For example, if there exist events M and N, the entire outcome for the events is M×N (Kaliraman, 2017).
The counting principle brings about a formula that enables us to determine the exact number of outcomes in a probability experiment even before drawing a tree diagram nor the sample space. The correctness of a tree diagram can thus be identified by the number of outcomes it brings about as compared to the fundamental counting principle. Conversely, a tree diagram visualizes how the occurrence of an event affects the other.
At the end of the day, we can conclude the fundamental counting principle to be the more convenient technique in identifying the total number of outcomes. The certainty and precision tree diagram is dependent on the counting principle, as elaborated above. Additionally, using the fundamental counting principle on a large number of events is easier to use than the tree diagram (Yuan, et al., 2016).
In summary, the tree diagram and the counting principle are the essential statistical methods that the theory of probability relies extensively on upon. In most cases, there exists great significance in knowing the total outcomes in a probability test. The tree diagram and the counting principle, therefore, helps predict a research investigation. Further analysis can henceforth be carried out using the attained results.
Work Cited
Kaliraman, Rajesh. “Unit-4 Techniques of Counting.” IGNOU, 2017.
Yuan, Chengjue, Dewei Li, and Yugeng Xi. “Medium-term prediction of urban traffic states using probability tree.” 2016 35th Chinese Control Conference (CCC). IEEE, 2016.