3. Mythic Quest is the most popular MMO in the gaming community. Suppose 62.5% of players purchase character en- hancements, 60% subscribe to the monthly newsletter that publishes hints and cheat codes, and 37.5% do both. (a) In a random group of ve players, what is the probability at most four subscribe to the monthly newsletter? (b) In a random group of four players, what is the probability at least one player purchases character enhancements? (c) In a random group of three players, what is the probability none of the players belong to both categories? (d) What is the probability a randomly selected player purchases character enhancements or subscribes to the monthly newsletter? (e) What is the probability a randomly selected player belongs to both categories or neither category? Interpret the result. (f) What is the probability a randomly selected player subscribes to the newsletter given he/she purchases character enhancements? (g) Are the events purchases enhancements and subscribes to newsletter independent? Justify