1. Mrs. Jones predicts that if it rains tomorrow it is bound to rain the day after tomorrow. She also thinks that the chance of rain tomorrow is 1/2 and that the chance of rain the day after tomorrow is 1/3. Are these subjective probabilities consistent with the axioms and theorems of probability?

2. In which of the following are events A and B mutually exclusive?

(a) Roll two dice. A is the event of a sum of 9; B is the event of a double (i.e., the same value on both dice).

(b) Draw 13 cards from a deck of 52 cards. A is the event of drawing at least one club; B is the event of drawing no aces.

(c) Toss a coin twice. A is the event of a head on the first toss; B is the event of a head on the second toss.