Geometry & Probability 8
Room 245
Class:
Name:
Date:
Homework for:
Unit 3
Probability
Probability
Guiding Concepts
In this unit, you will investigate chance processes and develop, use, and
evaluate probability models. At the end of the unit, you should be
able to:
 Understand that the probability of a chance event is a number between
0 and 1.
 Compare probabilities from a model to observe frequencies.
 Approximate or predict the probability of a chance event by collecting
data and observing the frequency of the event.
 Develop a probability model and use it to find probabilities of events.
 Find probabilities of compound events using organized lists, tables, tree
diagrams, and simulation.
Selected answers
1b.
¼
17.
1d.
0
3.
0/10, 3/10, 1/10,
3/10, 1/5
19.
4.
each has 1/6
probability
6.
37 goals
7a.
300
7b.
9.
1/26
43.
5/12
49.
no
51.
2/13
53.
½
59.
80%
61.
12/13
63.
11/13
9,000,000
21.
6,344,000 fewer
27a.
30
27b.
336
29.
41.
180, appetizer
combination
32.
5,985
39.
1/36
400
1/3
2
Geometry & Probability 8
Room 245
Class-BiN:
Name:
Date:
-
Introduction to Probability
1. A jar contains 6 red, 8 blue, one
white, 7 black, and two yellow
marbles.
2. A spinner is divided into 8
sections of equal size. The
sections are numbered 1
through 8.
Use this information to determine
the probability of selecting:
Use this information to determine
the probability of the needle
landing on:
a. a white marble
a. section 7
b. a red marble
b. an even numbered section
c. a yellow marble
c. section 1, 2, 3, or 4
d. a purple marble
d. section 9
e. a black marble
e. section 8
3
Experimental and Theoretical
Probability
3. A die is rolled 10 times and the
outcomes are:
4. A die is rolled. Complete the
table.
Outcome
Number of
Times
Roll 1
0
Roll 2
3
Roll 3
1
Roll 4
3
Roll 5
2
Roll 6
1
Roll Theoretical Probability
1
2
3
4
5
6
List the experimental probability
for rolling a:
Roll
Experimental
Probability
1
2
3
4
5
4
Geometry & Probability 8
Room 245
5. A spinner contains 8 equally
divided sections, two sections
have the letter A, 3 sections
have the letter B, one section
has the letter C, one section
has the D, and one section has
the letter E.
Draw a picture of the spinner
Use your drawing to fill in the chart
Spin Theoretical Probability
A
Class:
Name:
Date:
The spinner is spun 10 times and
the outcomes are:
Outcome Number of Times
A
4
B
1
C
3
D
2
E
0
List the experimental probability
for spinning a:
Spin
B
C
D
E
A
B
C
E
Experimental
Probability
Word Problems
8. A die is rolled. What is the
theoretical probability for rolling
a 3?
6. You made 8 out of 15 shots on
goal. Use experimental
probability to predict how many
goals you will make tomorrow if
you take 70 shots.
9. Mary rolls a die six times and
rolls a 3 on two of the rolls.
What is the experimental
probability for rolling a 3?
7. There are 1000 buttons in the
jar. You randomly select 10
buttons and get 3 red, 4 blue, 2
white, and 1 black. Use
experimental probability to
predict how many buttons in the
jar are:
10. Create a situation where the
experimental probability and
the theoretical probability have
the same value.
a. Red
b. Blue
c. White
d. Black
6
Geometry & Probability 8
Room 245
11. A coin is flipped.
a. What is the theoretical
probability for flipping a tail?
b. Mark and John flip a coin
twenty times and get
8 heads, 12 tails. What is the
experimental probability for
flipping a tail?
c. If Mark & John flip the coin
100 times, what do you think
will happen to the
experimental probability?
12. Bart makes 20% of his free
throws.
a. If he takes 500 free throws,
how many go in the basket?
b. Predict how many baskets
Bart makes when he takes
25 free throws.
Class:
Name:
Date:
13. A factory produces 1000
light bulbs per minute. Each
minute, one bulb produced will
be defective.
a. What is the theoretical
probability of selecting the
defective bulb from the light
bulbs produced in one
minute?
b. What is the theoretical
probability of selecting a
defective bulb from the light
bulbs produced in one hour?
14. Every 100th box of candy
contains a prize.
a. What is the theoretical
probability for selecting the
box of candy with a prize?
Fundamental Counting Principle
continued from #22…
b. A case contains 1000 boxes
and how many prizes?
17. A restaurant has 4
appetizers, 9 entrees, and 5
dessert choices.
a. How many meals are
possible?
c. What is the probability of
selecting a box containing a
prize a case?
b. If the restaurant wants to
increase their meals as
much as possible by adding
one more item, should they
add an appetizer, an entrée
or a dessert?
15. Create a situation where the
experimental probability is
greater than the theoretical
probability.
18. Martha has 8 shirts, 6 pair of
pants, and 4 different pair of
shoes. Assuming everything
matches, how many days can
Martha go without wearing the
same outfit?
16. How does understanding
probability help someone who
plays cards?
8
Geometry & Probability 8
Room 245
19. How many different 7 digit
telephone numbers are there, if
the first digit cannot be 0?
20. By adding an area code to
each 7-digit telephone number,
the phone company increased
the amount of telephone
numbers by how many?
(Remember that the first digit in
the area code and the phone
number itself cannot be 0.)
Class:
Name:
Date:
21. One state is considering
creating license plates where
letters cannot be repeated.
If the state has license plates
consisting of three letters,
followed by three different
digits, how many fewer license
plates are available when
repetition of letters is not
allowed?
22. A phone comes in 12
different colors, 5 different
headsets, and 7 different styles.
How many different phones are
available?
23. Mark is taking a 10 question,
True/False quiz. How many
different ways can the quiz be
answered?
25. Frank is calling his sister and
can’t remember the first two
digits of her phone number. He
remembers the remaining five
digits. What is the greatest
number of attempts that Frank
would have to make to
complete the call? (He knows
that the first digit of his sister’s
phone number is not 0.)
24. A combination lock has a
combination of 5 single digits,
none of which are repeated.
How many different
combinations are there?
26. A pizza parlor provides
customers with the opportunity
to create their own single
topping pizza by selecting from
4 different crusts, 5 different
sauces, 3 different cheeses,
and 15 different toppings.
a. How many pizzas are
possible?
b. If a second different topping
choice is allowed, how many
pizzas are possible?
10
Geometry & Probability 8
Room 245
Class-BiN:
Name:
Date:
-
Permutations and Combinations
27. Find the value of the
following:
a. 6P2
30. You must fit 10 out of 15
dogs in the cages along the wall
(one dog per cage). How many
different ways are there to place
them in the cages? This is an
example of a
________________________.
b. 8P3
c.
10P2
31. Find the value of the following:
a. 6C4
d. 3P3
b. 5C1
28. Thirty dogs and their
handlers enter a show ring. The
judge will pick 5 dogs to place in
the contest. How many different
ways can the first, second, third,
fourth, and fifth place be
awarded?
c. 4C4
d. 6C2
32. There are 21 girls on a
soccer team. Four of these girls
will be picked to be on the AllAmerican Team. How many
different groups of players can
be chosen?
29. You create a sundae with 3
out of 10 flavors at the Ice
Cream Store. This is an
example of a
________________________.
11
33. Find the value of the
following:
a. 10P6
36. Your parents inform you that
you can only invite 30 people out
of the 50 people that you wanted
to invite to your party. The
possibilities of the people you
can invite is an example of a
________________________.
b. 9P4
c. 5P5
37. Find the value of the
following:
a. 10C8
d. 4P1
b. 4C2
34. Twenty snowboarders enter a
race. The top 4 will get medals.
How many different ways can
the first, second, third, and
fourth medals be given?
c. 6C5
d. 3C3
38. There are 20 children in a
kindergarten class. Five of these
children will be picked for the
outstanding kindergarten award.
How many different groups of
kindergarteners can be chosen?
35. You must buy 3 kinds of soda
out of 8 at the store. This is an
example of a
________________________.
12
Geometry & Probability 8
Room 245
Class:
Name:
Date:
Probability of Compound Events
39. You are given a pair of dice.
One die is numbered 1 through
6 but the other die is numbered
7 through 12. What are the odds
of rolling a 3 and an 8?
40. A machine generates
numbers randomly from balls
numbered 5 through 15. Two
balls are selected, with
replacement. What are the odds
that both the numbers picked
will be 8?
41. A bag with 6 blue marbles, 3
green marbles, and 4 orange
marbles is lying on a table. What
is the probability that John will
pick 2 green marbles? (without
replacement)
42. What is the probability that
the first three cards drawn from
a full deck of cards are clubs?
(without replacement)
43. There are 6 male puppies
and 3 female puppies. What is
the probability that the first two
puppies chosen will be males?
(without replacement)
44. What is the probability that
the first three cards drawn from
a full deck of cards are kings?
47. A lottery machine generates
numbers randomly. Three
numbers are picked from 1 and
20. What is the probability that
all three numbers that are
picked are 17?
45. You dropped two coins. What
is the probability that they will
both land on heads?
48. There are 4 blue marbles and
2 red marbles. A marble is
selected and not returned. What
is the probability that two red
marbles will be chosen?
46. Bill Gates wrote a computer
program that generates three
random numbers from 1 and 10.
What is the probability that all
three values will be three?
14
Geometry & Probability 8
Room 245
Class:
Name:
Date:
Probabilities of Mutually Exclusive and Overlapping Events
49. Are these events mutually
exclusive?
52.
P(rolling a 2 or a 6) on a die
Event A: Roll an even number
Event B: Roll a prime number
50. Are these events mutually
exclusive?
53. P(rolling a 2 or an even
number) on a die
Event A: Select a bird
Event B: Select a bald eagle
54. Are these events mutually
exclusive?
Calculate:
51. P(selecting a queen or a 10)
from a deck of cards
Event A: Roll a number greater
than 2
Event B: Roll a number less than 3
55. Are these events mutually
exclusive?
57. P(rolling an odd number or a
number greater than 3) on a die
Event A: Select a consonant from
the alphabet
Event B: Select a vowel from the
alphabet
58. P(choosing a club or a black
card) from a deck of cards
Calculate:
56. P(choosing a 4 or a jack)
from a deck of cards
16
Geometry & Probability 8
Room 245
Class:
Name:
Date:
Complementary Events
59.
P(snow) = 20%
64.
P(no snow) =
60.
P(A) = 0.9
P(not A) =
61. What is the probability of not
selecting a queen from a deck of
cards?
62. What is the probability of not
rolling a 1 on a die?
63. What is the probability of not
selecting a queen or a king from
a full deck of cards?
P(rain) = 5%
P(no rain) =
65.
P(A) = 3/5
P(not A) =
66. What is the probability of not
selecting a four from a deck of
cards?
67. What is the probability of not
rolling a 6 on a die?
68. If 22% of the people in the
room are bald, what percent are
not bald?