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HSS-CP.A.1 WORKSHEET #1 – PATTERSON
Name: _____________________________
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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 – 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 – PATTERSON
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5. Use the fundamental counting principle to determine the sample space size.
a) A 5 digit combination lock that
uses values 0 – 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 don’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 – PATTERSON
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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 #’s = ___________________
P(the multiples of 4) = _______
P(prime #’s)c = _______
SHADE P(the multiples of 4)
SHADE P(prime #’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 – PATTERSON
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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) = ______