Alice and Daisy are playing a round of a dice game. Alice, the attacker, and rolls a fair 6-sided die (equal probability for any of 1, . . . , 6). Daisy, the defender, has home advantage. She rolls a fair 8-sided die (equal probability for any of 1, . . . , 8). The player that rolls the higher number wins the round. Let A be the result of Alice's die, and D be the result of Daisy's die.

 (a) Describe the sample space  of the rolls of the two dice.

 (b) What is the cardinality of the sample space, 

(c) Find P(D  7)

 (d) Find P (A > D) by counting. 

(e) Find P (A = D) by counting. 

(f) Calculate P(A < D) by the properties of set theory.