2. Piacentine-pattern playing cards are a type of Spanish-suited playing card used in Italy. A Placentine-pattern deck o

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2 Piacentine Pattern Playing Cards Are A Type Of Spanish Suited Playing Card Used In Italy A Placentine Pattern Deck O 1 (69.16 KiB) Viewed 25 times

2. Piacentine-pattern playing cards are a type of Spanish-suited playing card used in Italy. A Placentine-pattern deck of cards contains 40 cards, separated into 4 suits: Swords, Cups, Coins and Clubs. Each suit consists of 10 cards: 7 numeral cards (Ace, 2, 3, 4, 5, 6 and 7) and 3 character cards (Knave, Horse and King). Consider an experiment where a deck of Piacentine-pattern playing cards are properly shuffled, and then 1 card is dealt. We will use this experiment for the following questions. (a) What is the probability that the card dealt is a character card? (2 marks) (b) Now suppose that the card is returned to the deck, and that the deck is properly shuffled once more. Suppose we repeat the experiment of drawing 1 card, noting the card, returning the card to the deck, and then reshuffling the deck another 11 times (for a total of 12 times including the initial trial conducted in the preamble of question 2 above) Let X denote the number of character cards that are drawn from the 12 trials. List all the possible values that can be observed for X. (2 marks) (e) What is the expected frequency for the number of character cards dealt in the course of the 12 trials? Make sure to show all your workings. (2 marks) (d) Suppose that X = 6 is observed. What is the relative frequency for this many character cards being drawn? Make sure to show all your workings. (2 marks) (e) Now suppose that we shuffle our deck properly, and start our experiment again. Instead of conducting 12 trials however, we will now conduct n trials, where n is some positive integer. For a very large value of n, what should the relative frequency be approximately equal to for: i. The number of numeral cards with values 6 or higher that are dealt? (2 marks) ii. The number of Horse cards that are dealt? (1 mark) iii. The number of cards dealt that are not from the Swords suit? (1 mark)