cJean Marie Linhart 2008Math 166 Quiz 4 Take Home Fall 20 08Printed name:Row: Seat number:You may work together on this take-home quiz. You may use your calcu-lators, book, notes, and other supplementary mater ials of your choosing. Youmust show all your work to receive credit and partial credit on the questions.Write down and explain wha t you are calculating.You may staple extra sheets of paper to this quiz if you need extra room toshow your work.1) Recall the standard deck of 52 cards. A poker hand consists of 5 cards chosenfrom the deck regardless of order (order doesn’t matter). A pa ir is two cards ofthe same rank, e.g. the 4 of diamonds and the 4 of spades form a pair. A tripletis three cards o f the same rank, e.g. the 6 of hearts, the 6 of clubs and the 6 ofdiamonds form a triplet.a. (2 points) Find the number of ways of getting at least a pair in a poker hand,without any restrictions on the other 3 cards. Let this be event A.b. (2 po ints) Find the number of ways of getting at least a triplet in a pokerhand, without any re strictions on the other two cards. Let this be event B.c. (2 points) Can you get both a pair and a triplet in a poker hand? If so, findthe number of ways you can do this. Hint: this is A ∩ B.d. (2 points) What is the number of different poker hands in the event E =A ∪ B of getting a poker hand that has either a pair with no restrictions onthe remaining three cards or a triplet with no re strictions on the remaining twocards?e. (1 point) How many poker hands are there? (Hint: this is S, your s amplespace.)f. (1 point) What is the probability of the event E of getting a poker hand witheither a pair with no restrictions on the remaining 3 cards, or a triplet with norestrictions on the remaining two cards? Write your a ns wer to three significantfigures.2) Use the definitions in problem one. A quadruplet is all four of a kind, e.g. allfour 9s in the deck, the 9 of diamonds, 9 of hea rts, 9 of clubs and 9 of spades.a. (1 point ex tra credit) Find the number of ways of getting a pair in a pokerhand, where none of the re maining three car ds may form a triplet with the pairselected.b. (1 point extra credit) Find the number of ways of getting at least a triplet ina poker hand, where the remaining two cards may not form a quadruplet withthe triplet selected.c. (1 point extra credit) In this case, can you get both a pair and at triplet ina poker hand? How many ways are there of doing this?d. (1 point extra credit) What is the number of different poker hands in theevent E of getting a poker hand that has either a pair with the restriction aboveor a triplet with the restriction above?e. (1 point extra credit) What is the proba bility of the event E of g e tting eithera pair with the restriction above, or a triplet with the restriction above in apoker hand? Write your answer to three significant
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