Mark is a recreational hockey player who plays 25 games in a season. If Mark scores a goal in a game, he gets taken out for the remainder of the game (to alleviate his chronic back pain). The probability that Mark scores a goal during a game is 40%, independent of the previous games he has played. a) Calculate the probability that Mark doesn't score a goal in a given season. b) Calculate the probability that Mark scores at least 4 goals in a given season. c) Calculate the probability that Mark scores his 15th goal in his 18th season game. d) Suppose that Mark improves as a hockey player over the course of the season, and his chances of scoring a goal during a game increases as the number of games he plays increases. Would you still calculate your answers to the questions (a)-(c) above in the same way or would there be an issue with the distributions used? Carefully explain why or why not.