Final answer:
The statement that a decision tree is a graphical representation of a decision problem's logical structure in terms of decisions and outcomes is true. Decision trees are useful in probability, business, and machine learning. They visually represent potential outcomes and help with calculating probabilities.
Step-by-step explanation:
A decision tree is indeed a graphical representation of the logical structure of a decision problem, showing the sequence of decisions to be made and the possible outcomes. The statement given is true. Decision trees are widely used for various purposes, including probability calculations, business decision analysis, and machine learning.
To illustrate, let's consider a simple probability example using a tree diagram. Imagine an urn with 11 balls: 3 red and 8 blue. If we draw two balls one at a time, with replacement, we can represent all the possible outcomes with a tree diagram. Since the first ball is put back before drawing the second one, each draw is independent, meaning the outcome of the second draw is not affected by the first one.
A tree diagram helps visualize all potential outcomes, making it easier to calculate probabilities. For example, the probability of drawing a red ball and then a blue ball would be found by multiplying the individual probabilities along the branches of the tree that represent this outcome.
Beyond probability, phylogenetic trees and cladograms are used in biology to represent the evolutionary relationships between species. These are also types of tree diagrams, showing how species diverge from common ancestors over time.