1. Do you think that weather predictions ("the chance of rain tomorrow is 3 in 10") are better considered as theoretical probabilities or empirical probabilities? Explain.
2. Two honest dice are tossed.
(a) List the 36 ways the dice may fall (remember to distinguish between the outcome of die #1 and the outcome of die #2).
(b) Consider the sum of the points on the two dice; they may be from 2 to 12. With what relative frequency does each possible sum occur?
(c) What is the probability of obtaining a 1 with the first die and a 3 with the second die?
(d) What is the probability of obtaining a sum of points equal to 4?
(e) What is the probability of obtaining a sum of points equal to 7 on one toss?
(f) What is the probability of obtaining a sum of points greater than 7? Greater than 4?
(g) What is the probability of obtaining a sum of points equal to 7 on two successive throws? Of 2 points on two successive throws?