Each picture below represents a two-dimensional space where observations are classified into two categories. The categories are representing by light and dark shading. A classification tree is to be constructed for each space.

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Determine which space can be modeled with no error by a classification tree.

• I only
• II only
• III only
• I, II, and III
• The correct answer is not given by (A), (B), (C), or (D).

Copyright 2023. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.

Key: A

Each step must divide the one the existing regions into two parts, using either a vertical or a horizontal line. Only I can be created this way.

Copyright 2023. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.