Question

Subjective probabilities may or may not satisfy the third axiom of probability. When they do, we say that they are consistent; when they do not, they ought not to be taken too seriously.

(a) The supplier of delicate optical equipment feels that the odds are 7 to 5 against a shipment arriving late, and 11 to 1 against it not arriving at all. Furthermore, he feels that there is a 50/50 chance (the odds are 1 to 1 ) that such a shipment will either arrive late or not at all. Are the corresponding probabilities consistent?

(b) There are two Ferraris in a race, and an expert feels that the odds against their winning are, respectively, 2 to 1 and 3 to 1 . Furthermore, she claims that there is a less-than-even chance that either of the two Ferraris will win. Discuss the consistency of these claims.