A board game requires players to roll a pair of balanced dice for each player’s turn. Denote the outcomes by (die 1, die 2), such as (5, 3) for a 5 on die 1 and a 3 on die 2.
a. List the sample space of the 36 possible outcomes for the two dice.
b. Let A be the event that you roll doubles (that is, each die has the same outcome). List the outcomes in A, and find its probability.
c. Let B be the event that the sum on the pair of dice is 7. Find P(B).
d. Find the probability of (i) A and B, (ii) A or B, and (iii) B given A.
e. Are events A and B independent, disjoint, or neither? Explain.