Tom is considering purchasing a gaming platform. He has two choices: PlayStation 5 and Nintendo Switch. The cost of a PlayStation is $20 and the cost of a Nintendo Switch is $15. In the future, he will use the gaming platform to play a game. There are two games in consideration game X and game Y. A game may or may not be available on a gaming platform. We know that: (1) Game X is available on PlayStations with probability 0.6; it is available on Nintendo Switch if and only if it is not available on PlayStation 5; (2) Game Y is available on both PlayStation 5 and Nintendo Switch with probability 0.7; otherwise it is available on neither platform; (3) The availability of Game X and the availability of Game Y are independent, (4) Both games, if available, are free to play (5) Playing Game X gives Tom a happiness that worth $50; playing Game Y gives Tom a happiness that worth $40, (6) Due to time limitation, Tom can play at most one game. Answer the following questions: (a) Construct a decision tree for Tom. (5 points) (b) Which gaming platform should Tom purchase?
