Question: Consider a factory that produces cubes with side length between 1 and 3 cm. Alice's credence that the next cube from the factory will have

Consider a factory that produces cubes with side length between 1 and 3 cm. Alice's credence that the next cube from the factory will have side length less than 2 cm is 2/3, while her credence that it has volume greater than or equal to 8 cm³ is 3/4.

(i) Calculate Alice's subjectively fair odds for bets on the following hypotheses:

h1 = The next cube has side length less than 2cm

h2 = The next cube has volume greater than 8cm³

(ii) Suppose Alice accepts bets at her subjectively fair odds on both h1 and h2. Calculate how much money she wins and loses on each possible outcome.

(iii) What's gone wrong? (Be as specific as possible.) How is this kind of example related to the justification for Bayesian confirmation theory?

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