Final answer:
For Bayes' theorem, tree diagrams and Venn diagrams are helpful graphical displays that can assist in visualizing conditional probabilities, event sequences, and relationships between different sets.
Step-by-step explanation:
The student's question pertains to graphical displays that can assist with the application of Bayes' theorem when calculating probabilities. To answer this question: Tree diagrams and Venn diagrams are particularly helpful in visualizing conditional probabilities and can indeed be used in conjunction with Bayes' theorem.
A tree diagram is beneficial because it visually represents all possible outcomes of a probabilistic event in a structured, branch-like manner. This makes complex probability scenarios more manageable. For example, in an urn with red and blue balls, if you draw one ball at a time with replacement, a tree diagram can clearly demonstrate the different probabilities for each sequence of events.
The use of a Venn diagram can also be instrumental when using Bayes' theorem. Venn diagrams allow for straightforward visualization of relationships between different sets and their probabilities, such as the intersection (AND), union (OR), and conditional relationships (given that).
Another helpful tool would be a contingency table, also known as a two-way table, which organizes data according to two different, possibly dependent variables. Contingency tables make it easier to calculate not only direct probabilities but also conditional probabilities, which are central to Bayes' theorem.
Therefore, the correct option for a graphical display helpful when using Bayes' theorem to calculate a probability is either a tree diagram or a Venn diagram.