4. (30 marks) "Go" is one of the oldest games in the world. The objective is to control territory by placing pieces called "stones" on vacant points on the board. Players alternate placing their stones. The player using black stones goes first, followed by the player using white stones. The following table shows the result of a study about the advantage of playing first (i.e., using the black stones) in Go. Black Player Level Opponent Level Number of Wins Number of Games T 34 34 66 116 15 28 L 5 40 Total: 120 218 In this table, "T" represents the top-level players and "L" represents the low-level players. (a) Estimate the probability of winning when one plays first if we randomly select a game in the study. (3 marks) (b) Estimate the probability of winning when one plays first for each combination of the levels of players. (4 marks) (c) If we randomly select a game in the study and it is known that the players are at the same level, what is the probability that the black player wins? (3 marks) 3