2. (15 Points) We have a sample as follows: Gold (G) Silver (S) Bronze (B) Total US (U) 45 50 45 140 China (C) 40 40 45 125 Others (0) 35 30 30 95 Total 120 120 120 360 We define each outcome as "country X winning medal Y". (1) Write the sample space for this sample. (2) What is the probability a randomly selected medal is Gold or won by China? (3) What is the probability a randomly selected was silver and not won by the US? (4) Are the pair (U, S) mutually exclusive events? (5) Given a randomly selected medal is Gold, what is the probability that the medal was won by China? (6) Are the events U and S independent? To find the probability of sequential events: (7) Select 3 medals sequentially without replacement, what is the sample space for this experiment? (8) Draw a tree diagram for this experiment. (9) What is probability that the first is Silver, and contains at least one Gold medal?