In this case, outcomes at each trial are mutually exclusive and their union is the universal set (Sharma, 2007).

While Brenda is right in identifying the tree diagram as an aid to visualizing outcomes, her definition is not comprehensive. Direct calculation of probabilities is more efficient in simple outcomes such as single trials. The tree diagram is more applicable in visualizing outcomes of multiple trials. She also does not explicitly identify the fact that tree a diagram is suitable for independent trials. An example, similar to Brenda’s would involve independent and successive selection of a ball from a set of four white balls followed by another selection from a set of three blue ones. While she exhibits the first principles of probability such as determination of the probability space and additive and multiplicative rules, Brenda lacks sufficient mathematical terms for communicating her rich knowledge (Sharma, 2007).

Tami is explorative of the scope of a tree diagram and its role in identification of a sample space. Her example of possible application of a tree diagram is also adequate. This is because it identified selection of two items from two mutually exclusive sets. A good example that corresponds to Tami’s is a successive selection of a book from a set of five books, each with a different color, followed by selection of a pen from a set of three differently colored pens. Her answer also demonstrates an understanding in determination of sample space from trials. Though her response is commendable, she fails to expressly identify the independence property of trials that is a necessity for application of a tree diagram (Sharma, 2007).

Yvette’s answer that a tree diagram is a way of listing possibilities of a sequence is not very accurate. This is because of two reasons. First, a sequence may have a single outcome at each trial and may not fit ...Show more