please help

1. A hockey player attempts to shoot the puck and score a goal. c There is a 0.4 chance that the puck misses before it reaches the goalie. in If the puck does not miss, the probability that the goalie saves the puck is 0.8, otherwise it is a goal. 0 If the goalie does not save it (and it isn't a miss), the shot is a goal. (a) What is the probability that the goalie saves the puck? (b) What is the probability that the shot attempt is a goal? (c) Are the events (shot misses) and (goal is scored) independent? ) (d Are the events (shot misses) and (goal is scored) mutually exclusive? 2. 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 R of the rolls of the two dice. (b) What is the cardinality of the sample space, #9? (c) Find P(D 2 7) (d) Find P(A > D) by counting. (e) Find P(A = D) by counting. (f) Calculate P(A