Chapter 6.1, Problem 1PB

Rolling dice

1. a. State in a table the probability distribution for the outcome of rolling a balanced die. (This is called the uniform distribution on the integers 1, 2,…, 6.)
2. b. Two balanced dice are rolled. Show that the probability distribution for X = total on the two dice is as shown in the figure. (Hint: First construct the sample space of the 36 equally likely outcomes you could get. For example, you could denote the six outcomes where you get a 1 on the first die by (1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), where the second number in a pair is the number you get on the second die.)
3. c. Show that the probabilities in part b satisfy the two conditions for a probability distribution.