6.1 Rolling dice

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,c, 6.)

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.)

c. Show that the probabilities in part b satisfy the two conditions for a probability distribution.

P(x) 0.18 0.16 0.141 0.12 0.10 0.08 0.06 0.041 0.02 2 6 I 00 8 10 12