If subjective probabilities are determined by the method suggested in Exercise 2.16, the third postulate of probability may not be satisfied. However, proponents of the subjective probability concept usually impose this postulate as a consistency criterion; in other words, they regard subjective probabilities that do not satisfy the postulate as inconsistent.
(a) A high school principal feels that the odds are 7 to 5 against her getting a $ 1,000 raise And 11 to 1 against her getting a $ 2,000 raise. Furthermore, she feels that it is an even- money bet that she will get one of these raises or the other. Discuss the consistency of the corresponding subjective probabilities.
(b) Asked about his political future, a party official replies that the odds are 2 to 1 that he will not run for the House of Representatives And 4 to 1 that he will not run for the Senate. Furthermore, he feels that the odds are 7 to 5 that he will run for one or the other. Are the corresponding probabilities consistent?