HSS-CP.A.1 WORKSHEET #1 вЂ“ PATTERSON Name: _____________________________ 1 1. Determine the sample space by listing the elements of the sample space in set notation and then determine the number of possible outcomes in that sample space. a) The rolling a 8 sided (D8) die. b) The possible genders of the two children in a family. c) The factors of 12 _______________________ _______________________ _______________________ d) The letters in the word, Golf. e) The digits in the number, 13430 f) Rolling a dice with sides of 1, 3, 4, 3, 3, 1 _______________________ _______________________ _______________________ 2. Determine whether the sample spaces in question #1 are uniform or not. a) Uniform or Not Uniform b) Uniform or Not Uniform c) Uniform or Not Uniform d) Uniform or Not Uniform e) Uniform or Not Uniform f) Uniform or Not Uniform 3. Create a tree diagram for the following. Determine the elements and size of the sample space and whether it represents uniform or non-uniform probabilities. a) the possible genders of having three children b) selecting an outfit at random from 3 shirts (v neck, collar, and t-shirt) and 2 pants (jean and dockers). Size = ______ Size = ______ Uniform or Not Uniform 4. Jeff and Sally are playing Paper вЂ“ Scissors - Rock. It is a game where each person displays a symbol (flat hand (paper), split finger (scissors) or fist (rock)) at the exact same time. The winner is determined by paper beats rock, scissors beat paper, and rock beats scissors. Use the table to display the sample space for the game. a) How many elements in this sample space? ______ Uniform Sally (Rock) or Not Uniform Sally (Paper) Sally (Scissors) Jeff (Rock) Jeff (Paper) Jeff(Scissors) b) How many ways can Jeff win? ________ HSS-CP.A.1 WORKSHEET #1 вЂ“ PATTERSON 2 5. Use the fundamental counting principle to determine the sample space size. a) A 5 digit combination lock that uses values 0 вЂ“ 5 b) A multiple choice test has 5 questions (each question has 4 possible selections) c) The different type of sandwiches if you can pick from bread (white, wheat, rye), meat (ham, turkey, roast beef), and filler (pickles, lettuce, tomatoes, peppers, olives). 6. A student is creating a course schedule of 7 Calculus classes, 5 Psychology classes, and 3 Chemistry classes that donвЂ™t conflict with each other. How many different schedules are possible? 7. License plates in most states have 3 alphabetic values followed by 3 numeric values. If there are not restriction the plates, what is the total number of plates possible? 8. Police use photographs of various facial features to help witnesses identify suspects. One basic identification kit contains 210 hairlines, 77 eyes and eyebrows, 85 noses, 121 mouths, and 70 chins and cheeks. The developer of the identification kit claims that it can produce billions of different faces. Is this claim correct? 9. Determine the basic probability. a) Given a standard deck of cards, what is the : P(Diamond) = __________ P(Jack) = __________ P(Numerical Card) = __________ P(Ace) = __________ P(Face Card) = __________ P(Red 8) = __________ b) Given that a family has 3 children, what is the: a) P(three boys) = __________ b) P(Boy, Girl, Boy) in that order = __________ c) Given the roll of 2 dice and their values are summed, what is the: P(sum of 12) = __________ P(sum of 7) = __________ P(sum of 4) = __________ P(even sum) = __________ HSS-CP.A.1 WORKSHEET #1 вЂ“ PATTERSON 3 10. Given the sample space, Set U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}. -- determine the elements of the following subsets -- draw a Venn diagram of the subset -- determine the probability -- shade the required region a) Set B = the multiples of 4 = ___________________ c) Set P = prime #вЂ™s = ___________________ P(the multiples of 4) = _______ P(prime #вЂ™s)c = _______ SHADE P(the multiples of 4) SHADE P(prime #вЂ™s)c 11. Determine the probability. a) P(A) = 0.4 P(Ac) = ______ b) P(A) = 0.78 P(Ac) = ______ c) P(A) = 3 7 P(Ac) = ______ 12. Given the sample space, Set U = numbers 1 to 20 a) Set A = the multiples of 6 = ___________________ Set B = # greater than 16 = ___________________ Mutually Exclusive? Yes or No b) Set A = factors of 8 = ___________________ Set B = factors of 18 = ___________________ Mutually Exclusive? Yes or No P(multiple of 6) = ________ P(factor of 8)c = ________ P(# greater than 16) = ________ P(factor of 18)c = ________ Set A Set B = __________ P(multiple of 6 and greater than 16) = ______ What is Set A Set B? _________________ P(multiple of 6 or greater than 16) = ______ SHADE Set A Set B What is Set A Set B? __________ P(factor of 8 and factor 18) = ______ What is Set A Set B? _______________________ P(factor of 8 or factor 18) = ______ SHADE Set Bc HSS-CP.A.1 WORKSHEET #1 вЂ“ PATTERSON 4 13. Given the sample space U = natural numbers from 1 to 20, determine which of the following diagrams represents the relationship of the two defined subsets. Relationship #1 Relationship #2 Relationship #3 Relationship #4 a) Set A = even numbers Set B = odd numbers Relationship # ______ b) Set A = factors of 12 Set B = factors of 10 Relationship # ______ c) Set A = even numbers Set B = {2, 8, 10} Relationship # ______ d) Set A = multiples of 3 Set B = Factors of 14 Relationship # ______ e) Set A = numbers < 5 Set B = numbers < 10 Relationship # ______ 14. Shade the region. a) Set A c) Set Bc (NOT B) e) Set A (A OR B) h) Set B Set Ac (B AND Not A) d) Set A Set Bc (A AND Not B) Set B g) (Set A Set B)c Not (A OR B) 15. Place the values in the Venn diagram and determine the missing probability. a) P(A AND B) = 0.12 b) P(A AND B) = 0.25 P(A) = 0.53 P(B) = 0.70 P(A AND Not B) = ______ P(B AND Not A) = ______ c) P(A OR B) = 0.7 d) P(A OR B) = 0.8 P(A) = 0.53, P(B) = 0.37, P(B AND Not A) = ______ P(A AND Not B) = ______