Section 1.10 - Critique of the Model

The probability model is based on finite, symmetric sample spaces, which are easy to manipulate and provide simple outcome-probability calculations. However, using rational numbers for ratios can be limiting,^?For example, it is unlikely that the probability that a flipped thumb tack lands point up is expressible a ratio. as can unbounded sample spaces.^?For example, the probability that a sequence of coin tosses eventually produces a heads has potentially unbounded outcome length.

Separating the probabilistic model from its mathematical underpinnings promotes philosophical clarity, and emphasizes that the mathematics have wider use than just supporting the model. Also missing is the connection between the model based on sample-space symmetry and the intuitive frequency-based probability interpretation; Section 2.8 makes the connection.