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Part B: Answers should include full solutions from this point onward. Communication marks will be awarded for clear, complete steps using proper notation. (33 Marks) 12) You play a 2-stage game called: Royal Route. (9 marks) Stage 1: You pick a card from the deck to determine your path in stage 2. If you pick a face-card you are onto the "Royal Rumble". If you pick an odd number card you get to play "Odd Balls". If you pick an even number card you win "Even Steven" which rewards you with $2 and you do not continue to stage 2. Stage 2: In the "Royal Rumble" you flip 2 coins. If you get 1 head you win $3, if you get 2 heads you win $5, if you get no heads then "off with your head - no money for you"! In "Odd Balls" you pick a ball out of a royal satchel. In the satchel are 4 balls that say "peasant" for which you win no money, there are 2-balls that say "duke/duchess" for which you win $3, and there is 1 ball that says "king/queen" which wins you $10. a) Define the random variable AND state its unit of measure. b) Create a fully labelled probability tree diagram to represent this situation. c) Create a probability distribution table. d) Determine the expected value (you may use your table from part c to show your work) AND state what it represents in the context of the