Kim is playing a card game, In this game a hand of 5 cards is dealt randomly to her by her friend Liz from a well-shufed pack of 52 cards. There are 4 ace cards in the pack of 52 cards: A A A A 9 L Q Q a f O O V V V V If Kim gets three or four ace cards in her hand of 5 cards, she will win $15, if she gets one or two ace cards in her hand of 5 cards, she will win 85, but if she gets no ace cards in her hand of 5 cards, she needs to pay Liz $10. a) How many different selections of 5 cards are possible? Answer: [1 mark] h) (i) In how many ways can her hand of 5 cards contain no ace cards? Answer: [1 mark] (ii) In how many ways can her hand of 5 cards contain at least three ace cards? Answer: [1 mark] c) Let G be the amount Kim gains by playing this game. Complete the following probability distribution for G, giving all probability values correct to 4 decimal places: [3 marks] d) Use your values from part c) to calculate the expected gain $ E(G). $ E(G) = $ [1 mark] e) This game [1 mark]