Download Basic Concepts of Probability - Richland School District Two

Chapter 5 – Probability
Student _______________
SAVE this sheet. You will need it for the entire chapter.
Complete the chart to find the sample space for rolling two dice.
Die 2
Die 1
1
2
3
4
5
6
1
(1,1)
(2,1)
(3,1)
(4,1)
(5,1)
(6,1)
2
(1,2)
(2,2)
(3,2)
(4,2)
(5,2)
(6,2)
3
(1,3)
(2,3)
(3,3)
(4,3)
(5,3)
(6,3)
4
(1,4)
(2,4)
(3,4)
(4,4)
(5,4)
(6,4)
5
(1,5)
(2,5)
(3,5)
(4,5)
(5,5)
(6,5)
6
(1,6)
(2,6)
(3,6)
(4,6)
(5,6)
(6,6)
black
red
Complete the chart for an ordinary deck of cards.
 hearts
diamonds
spades
clubs
A
2
3
4
5
6
7
8
9
10
J
Q
K
A
2
3
4
5
6
7
8
9
10
J
Q
K
A
2
3
4
5
6
7
8
9
10
J
Q
K
A
2
3
4
5
6
7
8
9
10
J
Q
K
Elementary Statistics: Picturing the World - Prentice Hall
Created by Tina McRae for Ridge View High School
Probability & Statistics A# 5.1
Basic Concepts of Probability
Student ____________________
1.
What is a sample space?
2.
What are the possible values of the probability of an event?
3.
When an event is certain to occur, what is its probability?
4.
When an event cannot happen, what is its probability?
5.
If the probability that it will rain is 0.45, what is the probability that it
will not rain?
6.
Circle the numbers that could represent the probability of an event.
a) 0
7.
b) 1.5
c) – 1
d) 50%
e) 2/3
Explain why the following statement is incorrect.
The probability of rain tomorrow is 120%.
A computer is used to randomly select a number between 1 and 2000. Decide
whether the event is a simple event or not. Explain your reasoning.
8.
Event A is selecting 359.
9.
Event B is selecting a number less than 200.
List the sample space of each probability experiment.
10.
guessing the last digit in a telephone number
11.
guessing the day of the week a person was born
12.
determining a person’s grade level (9, 10, 11, 12) and gender (male,female).
Elementary Statistics: Picturing the World - Prentice Hall
Created by Tina McRae for Ridge View High School
You are planning a three-day trip. Use the following tree diagram to complete
the list of possible outcomes (sample space) and answer the questions.
Tree Diagram for Rainy Days
Day 1
Day 2
Day 3
Outcomes
13.
List the outcome(s) of the event
“It rains all three days.”
14.
List the outcome(s) of the event
“It rains on exactly one day.”
15.
List the outcome(s) of the event
“It rains on at least one day.”
SSS
SSR
16.
You roll one die and flip a coin. Construct a tree diagram to show all
possible outcomes.
17.
You take a quiz containing three true-false questions. Construct a tree
diagram to show all possible outcomes.
18.
Students are classified by grade level (freshman, sophomore, junior, senior)
and gender (male, female) and eye color (blue, brown, green). Construct a
tree diagram.
Elementary Statistics: Picturing the World - Prentice Hall
Created by Tina McRae for Ridge View High School
Probability & Statistics A# 5.2
Basic Concepts of Probability
Student ____________________
If you draw one card from a standard deck of 52 playing cards, find the
following theoretical probabilities.
1.
P(a club) =
2.
P(a black card) =
3.
P(a queen) =
4.
P(a face card) =
Use a standard deck of 52 playing cards. Shuffle them well and count out 25
cards without looking at them. Put aside the remaining cards. You are going to
perform an experiment to estimate the probability of drawing a club, a diamond,
a heart, and a spade.
A. Draw one card and record its suit in the chart below.
B. Replace the card and shuffle the 25 cards.
C. Draw another card and record its suit.
D. Repeat the steps until you have recorded a total of 25 draws.
Clubs
Diamonds
Hearts
Spades
Total
25
Use your data to find the following experimental probabilities.
5.
What is the probability of you drawing a club from your 25 cards?
6.
What is the probability of you drawing a diamond from your 25 cards?
7.
What is the probability of you drawing a heart from your 25 cards?
8.
What is the probability of you drawing a spade from your 25 cards?
Now, look at your 25 cards. Count the number of cards in each suit.
Clubs
Diamonds
Hearts
Spades
Find the theoretical probabilities based on your 25 cards.
9.
P(club) =
10.
P(diamond) =
11.
P(heart) =
12.
P(spade) =
13.
Suppose you had recorded a total of 2,500 draws (instead of 25) in your
experiment. What does the Law of Large Numbers tell us about our
experimental probabilities and the theoretical probabilities?
Elementary Statistics: Picturing the World - Prentice Hall
Created by Tina McRae for Ridge View High School
Two coins are
Trial
1 2
Coin 1 H T
Coin 2 T T
flipped 20 times with the
3 4 5 6 7 8 9
H H T H T T H
H H H T T H T
following results:
10 11 12 13 14 15 16 17 18 19 20
T H T T H T H H T H T
T T T T H H T H T T H
According to the data, find the following experimental probabilities.
14.
P(both coins are alike) =
15.
P(both coins are heads) =
16.
P(at least one coin is heads) =
17.
P(neither coin is heads) =
18.
P(both coins are tails) =
19.
P(at least one coin is tails) =
20.
P(neither coin is tails) =
21.
P(both coins are different) =
The results of spinning a spinner with regions A, B, C, D, and E are given in the
table below.
D
C
E
Region
A B C D E
Frequency 15 7 11 8 9
B
A
22.
Do you think it is equally likely for the spinner to land in any region of the
spinner? Explain.
Theoretical
probability
23.
P(landing in region A) =
24.
P(landing in region B) =
25.
P(landing in region C) =
26.
P(landing in region D) =
27.
P(landing in region E) =
Experimental
probability
Find the theoretical probability when two ordinary 6-sided dice are rolled.
28.
P(both even) =
29.
P(one odd and one even) =
30.
P(doubles) =
31.
P(sum of 12) =
Elementary Statistics: Picturing the World - Prentice Hall
Created by Tina McRae for Ridge View High School
Probability & Statistics A# 5.3
Basic Concepts of Probability
Student ____________________
Classify the statement as an example of theoretical, experimental, or subjective
probability.
1.
According to company records, the probability that a washing machine will need
repairs during a six-year period is 0.10.
2.
The probability of choosing six numbers from 1 to 40 that match the six
numbers by a state lottery is 1/3,838,380 ≈ 0.00000026.
3.
The probability of a student sitting on a desk sometime today is 0.25.
Use the diagram to answer the question.
4.
What is the probability that a student
chosen at random…
a) wore blue jeans? b) did not wear blue jeans?
5.
What is the probability that a student
chosen at random
a) have Cingular?
b) do not have Cingular?
About
50
wore blue
jeans
About 60
wore some
other type
of pants
About
35 had
Cingular
service
About
70 had a
different
type of
service
When two pink flowers (RW) are crossed, there are four equally likely possible outcomes
for the genetic makeup of the offspring: red (RR), pink (RW), pink (WR), and white
(WW). Complete the Punnett square. If two pink flowers are crossed, what is the
R
W
probability that the offspring is …
6.
pink?
7.
red?
8.
R
white?
W
There are six types of coloring in registered collies. The Punnett square shows the
possible coloring of the offspring of a trifactored sable merle collie (SsMm) and a
trifactored sable collie (Ssmm).
9.
What is the probability that the
offspring has the same coloring as
one of its parents: SsMm and Ssmm?
SM
Sm
sM
sm
Sm
SSMm
SSmm
SsMm
Ssmm
Sm
SSMm
SSmm
SsMm
Ssmm
sm
SsMm
Ssmm
ssMm
ssmm
sm
SsMm
Ssmm
ssMm
ssmm
Elementary Statistics: Picturing the World - Prentice Hall
Created by Tina McRae for Ridge View High School
A company selects employees for random drug tests and uses a computer to
select employee numbers that range from 1 to 100. Find the probability of
selecting a number…
10.
less than 10
11.
greater than 10
12.
divisible by 10
13.
that is not divisible by 10
The distribution shows the number of workers of one company according to age.
Find the probability that a worker chosen at random is…
14.
between 21 and 24 years old
15.
between 35 and 44 years old
16.
not between 18 and 20 years old
17.
not between 25 and 34 years old
Age
Frequency
18 to 20 years old
21 to 24 years old
25 to 34 years old
35 to 44 years old
45 to 64 years old
65 years old and over
10
13
40
43
53
31
The pie chart shows the number of students who reported that their favorite
math class. Use the pie chart to find the probability that a student chosen at
random was…
Ridge View High School
Favorite Math Class
18.
a student who likes
Prob & Stats best
19.
a student who likes
geometry best
20.
a student who does not
like Prob & Stats best
21.
a student who does not
like geometry best
Prob & Stats
150
Geometry
35
Algebra 1
5
Algebra 2
10
The table shows the approximate U.S. age distribution from the 2000 Census.
Use the table to determine the probability of the event.
19 and under
20-34
35-59
60-84
85 and over
Age
29%
21%
34%
15%
1%
Population
22.
What is the probability that a randomly selected person in the U.S. will be at
least 20 years old?
23.
What is the probability that a randomly selected person in the U.S. will be less
than 60 years old?
Elementary Statistics: Picturing the World - Prentice Hall
Created by Tina McRae for Ridge View High School
Probability & Statistics A# 5.4
Basic Concepts of Probability
Student ____________________
List the outcomes of the event.
(Draw a tree diagram to help with #1. You have a chart to help you with #2.)
1.
Tossing three coins and getting 2 tails
2.
Rolling two six-sided dice and getting a sum of 4 or 5
Identify key words that help you classify each statement as theoretical,
experimental, or subjective probability. What type of probability is described?
3.
Based on research, a quality control officer says there is a 0.05 probability that
a randomly chosen part is defective.
4.
The probability of randomly selecting five cards of the same suit (a flush) from
a standard deck is about 0.002.
5.
The chance that Corporation A’s stock price will fall today is 75%.
6.
According to a study, the probability of a person from the U.S. being left
handed is 11%.
7.
The probability of rolling two six-sided dice and getting a sum greater than
nine is 1/6.
8.
According to the weather man, the probability of rain is 40%.
9.
If a die is rolled one time, find the probability of…
10.
a) getting a 4
b) getting an even number
c) getting a number greater than 4
d) getting a number less than 7
If one card is drawn from a deck, find the probability of …
a) getting an ace
b) getting a diamond
c) getting an ace of diamonds
d) getting a 4 or 6
e) getting a face card
f) getting a red card
Elementary Statistics: Picturing the World - Prentice Hall
Created by Tina McRae for Ridge View High School
11.
If one person is selected from a class of 5 girls and 10 guys, find the probability
that the person is a girl.
12.
A survey found that 58% of Americans think that U.S. military should be pulled
out of Iraq. If an American is selected at random, find the probability that he
or she will disagree or have no opinion on the issue.
13.
A couple plans to have three children. Construct a tree diagram and list
the sample space. Find the probability that they will have…
14.
a) all boys
b) exactly two boys
c) at least one boy
d) at least one child of each gender
Identify the complement of each event. Calculate the probability of the
event and the probability of its complement.
a) rolling a die and getting a 4
P(E)=
b) selecting a letter of the
alphabet and getting a consonant
P(E)=
c) selecting a day of the week
and getting a weekday
P(E)=
complement:
P(E’)=
complement:
P(E’)=
complement:
P(E’)=
Elementary Statistics: Picturing the World - Prentice Hall
Created by Tina McRae for Ridge View High School
Probability & Statistics A# 5.5
Counting Principles
Student _________________
1.
When you use the Fundamental Counting Principle, what are you counting?
2.
On the space shuttle, astronauts eat a meal that consists of a main dish, a
vegetable, and a dessert. If they can choose from ten main dishes, eight
vegetable dishes, and thirteen desserts, how many different meals are possible?
3.
A menu has three choices for salad, five main dishes, and two desserts. How
many different meals are available if you select a salad, a main dish, and a
dessert?
4.
In how many ways can a six-question true-false quiz be answered?
5.
In how many ways can a six-question multiple choice test be answered if each
question has choices A, B, C, and D?
6.
A coin is tossed eight times. How many different outcomes are there?
7.
Every person in the U.S. must have a unique social security number. How many
social security numbers are possible? __ __ __ - __ __ - __ __ __ __
8.
How many telephone numbers are possible that begin with the prefix 865?
865 - __ __ __ __
9.
How many telephone numbers are possible that begin with an 803 area code?
(803) __ __ __ - __ __ __ __
10.
Explain why some cities have more than one prefix number or some states have
more than one area code.
Elementary Statistics: Picturing the World - Prentice Hall
Created by Tina McRae for Ridge View High School
11.
How many five-digit zip codes are possible if digits can be repeated?
12.
How many five-digit zip codes are possible if digits cannot be repeated?
13.
How many five-digit zip codes are possible if digits can be repeated but the
first digit must be a 2?
14.
The call letters of a radio station must have four letters. The first letter must
be a K or a W. How many different station call letters can be made if repetition
is not allowed?
15.
How many different station call letters can be made if repetition is allowed?
16.
In a certain state, license plate numbers consist of two letters followed by a
four-digit number. How many different license plates can be formed if there
are no restrictions?
17.
For the same state, how many different license plates can be formed if the
letters O and I can not be used?
18.
The access code for a car’s security system consists of four digits. The first
digit cannot be zero and the last digit must be odd. How many different codes
are available?
19.
In how many ways can the letters A, B, C, D, and E be arranged for a threeletter security code if letters can be repeated?
20.
In how many ways can the letters A, B, C, D, and E be arranged for a threeletter security code if letters can not be repeated?
Elementary Statistics: Picturing the World - Prentice Hall
Created by Tina McRae for Ridge View High School
Probability & Statistics A# 5.6
Counting Principles
Student _________________
Probability & Statistics A# 5.7
Counting Principles
Student _________________
Write out what each expression means.
1.
5!
2.
8!
3.
10!
Write out the factorial fraction.
4.
5.
6.
18P6
65P3
29P5
Show your work.
7.
There are five steps involved in assembling a certain product. These steps can
be performed in any order. If management wants to find which order is the
least time consuming, how many different orders will have to be tested?
8.
In how many ways can a team of ten players line up in a row to pose for a photo?
9.
How many four-digit PINs are possible if digits cannot be repeated?
10.
In how many ways can the letters A, B, C, D, E, and F be arranged for a threeletter security code if letters can not be repeated?
11.
A horse race has eight entries. In how many different ways can the horses
finish first, second, and third if there are no ties?
12.
The starting lineup for a baseball team consists of nine players. Each member of
the team can play each position. In how many different ways can the starting
lineup be filled for a team of fifteen players?
13.
From a pool of fifteen candidates, the offices of president, vice-president,
secretary, and treasurer will be filled. In how many different ways can the
offices be filled?
14.
From a class of twenty students, how many different ways can the 1st, 2nd, and
3rd students be chosen?
15.
From a group of thirty candidates, the offices of president, vice-president,
secretary, treasurer, and historian will be filled. In how many different ways
can the offices be filled?
1.
What is the difference between a permutation and a combination?
Permutation or Combination?
2.
3.
4.
5.
the number
the number
the number
the number
of ways 10 people can line up in a row for concert tickets
of ways a four-member committee can be chosen from 15 people
of ways five photographs can be arranged on a shelf
of ways a person can select 8 songs from 15 available songs
Show your work.
6.
7.
8.
9.
A landscaper wants to plant four oak trees, eight maple trees, and six popular
trees along the border of a lawn. If the trees are evenly spaced apart, in how
many distinguishable ways can they be planted?
In how many distinguishable ways can the letters in STATISTICS be arranged?
In how many distinguishable ways can the letters in MISSISSIPPI be arranged?
From a group of 40 people, in how many different ways can a jury of 12 people
be selected?
Elementary Statistics: Picturing the World - Prentice Hall
Created by Tina McRae for Ridge View High School
10.
In order to conduct an experiment, four subjects are randomly selected from a
group of 20 subjects. How many different groups of four subjects are possible?
11.
A pizza shop offers eight toppings. If no topping is used more than once, in how
many different ways can a three-topping pizza be formed?
12.
A lottery has 52 numbers. In how many different ways can a group of six of the
numbers be selected?
13.
How many ways can 5 cards be selected from a standard deck of 52 cards?
14.
Use a combination to determine how many basketball games must be played in a
9-team league so that each team plays every other team one time.
15.
There are 23 students in a club. How many ways can 4 representatives be
selected?
16.
There are 20 boys on the team. How many ways can 5 boys be randomly chosen
for today’s basketball game?
17.
How many ways can a person select 1 soft drink and 2 snacks if there are
6 soft drink choices and 15 snack choices from the vending machine?
18.
In a repair shop there are 7cars and 4 pickups. In how many ways can a
mechanic select 3 cars and 2 pickups to repair?
19.
Suppose the Senate of the U.S. consisted of 58 Democrats and 42 Republicans.
How many committees consisting of 6 Democrats and 4 Republicans could be
formed?
Write out the factorial fraction. Use your calculator to evaluate each expression.
20.
21.
22.
18C5
55C3
29C9
23.
P
24.
P
25.
18 5
55 3
29P9
26.
Which answer is always higher? Explain why you think this happens.
Probability & Statistics A# 5.8
Counting Principles & Probability
1.
2.
3.
4.
5.
6.
7.
8.
9.
Student _________________
How many ways can a teacher choose ten test questions from a pool of fifty
questions?
How many ways can a teacher arrange ten test questions for a test?
How many different ways can a student answer ten true-false test questions?
What is the probability that a student answers all of the questions without even
reading the questions and gets a perfect score? (Hint: how many answer keys
will the teacher make for the test?)
How many ways can 20 students be arranged in a list?
From a class of 20 students working problems on the board, how many ways can
the 1st, 2nd, 3rd, and 4th students be arranged?
How many ways can a group of 4 students be chosen from a class of 20 students
to work problems on the board?
Because you are special, you must be part of the committee. How many ways can
this group of 4 students be chosen from a class of 20 students if you must be
one of the students?
What is the probability that you are chosen as a group member randomly?
Elementary Statistics: Picturing the World - Prentice Hall
Created by Tina McRae for Ridge View High School
How many ways can you arrange the letters A
H M T be arranged?
What is the probability that you arrange the letters from problem #10 with
your eyes closed and spell MATH ?
12.
How many ways can you choose a PIN for your saving account that consists of
4 digits (1-9) ?
13.
What is the probability that someone chooses the PIN number of 1234 ?
14.
What is the probability that someone chooses the PIN number that begins with
the number 1 ?
A bag of candy contains red, blue, and white M&M's. Construct a tree diagram to
show the possible outcomes for selecting three candies from the bag.
15.
How many outcomes are possible?
16.
What is the probability that I get
2 blues in my selection?
17.
What is the probability that I get
white in my selection?
18.
What is the probability that I get
at least 1 red in my selection?
19.
What is the probability that I get
one of each color in my selection?
10.
11.
A couple plans to have 3 children. Construct a tree diagram to show the possible
outcomes for the gender sequences of their three children.
20.
How many outcomes are possible?
21.
What is the probability that they
have 2 boys and 1 girl?
22.
What is the probability that they
have 2 girls and 1 boy?
23.
What is the probability that they
have at least one boy?
24.
What is the probability that they
have all one gender?
Elementary Statistics: Picturing the World - Prentice Hall
Created by Tina McRae for Ridge View High School
Probability & Statistics A# 5.9
Counting Principles
Student _________________
True or false?
1.
T
F
A customer can order a sundae with vanilla or chocolate ice cream
and with or without M&Ms. The number of possible sundaes would
be six.
2.
T
F
If five coins are tossed, there are 10 possible outcomes.
3.
A drawer contains white (W), Purple (P), and Black (B) socks. Two socks are
selected in the dark without replacement. Construct a tree diagram, list all the
possible outcomes.
a) How many outcomes are possible?
b) How many outcomes match the event:
“two socks are the same color”
c) What is the probability of reaching
into the drawer in the dark and pulling
out two socks that are the same color?
Write out how you obtain your answer for each of the following situations.
4.
The artist has two choices of paint: acrylics and oil. The artist has five choices
of colors: red, yellow, green, blue, and black. If the artist selects a type of
paint and then a color, how many possibilities will there be?
5.
A teenager has 8 tee shirts, 2 belts, and 5 pairs of jeans. How many different
outfits can he wear, assuming that he must wear a belt to keep those pants up
and keep that shirt tucked in?
6.
The password for an e-mail account has to consist of three letters of the
alphabet followed by two digits. How many different passwords can be selected?
7.
Using the numbers 0, 2, 4, 6, 8, you want to construct a three-digit pass
number. How many different numbers can be constructed if repetitions are
allowed?
8.
A license plate must have three letters, followed by three digits. The first
letter must be a W. How many different license plates are available if repetition
is allowed?
Elementary Statistics: Picturing the World - Prentice Hall
Created by Tina McRae for Ridge View High School
9.
A teacher gives an 8 question true-false quiz. If a student guesses on each
question without even reading the questions, how many different ways could the
quiz be answered?
How many of those ways are correct?
10.
A nurse has 6 patients to visit. How many different ways can she make her
rounds if she visits each patient only once?
11.
How many ways can 10 motorcycles can be parked in a row?
12.
How many distinguishable ways can 2 blue, 3 black, and 5 purple motorcycles be
parked in a row?
13.
There are 10 motorcycles in a race, how many ways can the motorcycles come in
1st, 2nd, and 3rd?
14.
There are 10 motorcycles, how many ways can 4 of them be selected for a testride?
15.
If 16 dogs are entered in a dog show, in how many ways can they be arranged in
a row for a picture?
16.
If 16 dogs are entered in a dog show and 5 are Collies, 7 are Poodles, and 4 are
German Shepards, then how many distinguishable ways can they be arranged in a
row for a picture?
17.
If 16 dogs are entered in a dog show, in how many ways can the judges award
1st, 2nd, 3rd, and 4th places?
18.
If 16 dogs are entered in a dog show, how many ways can 4 of them be chosen to
circle the show ring for the judges?
19.
In a vending machine, there are 4 drink choices and 10 snack choices. How many
different possibilities do I have if I want 1 drink and 2 snacks?
20.
In a class of 8 guys and 3 girls, a group of 2 guys and 1 girl is chosen to do a
project. How many different possible groups can be formed?
Elementary Statistics: Picturing the World - Prentice Hall
Created by Tina McRae for Ridge View High School
Probability & Statistics A# 5.10
Counting Principles
Student _________________
True or false?
1.
T
F
A club has 12 members. There are 1320 ways that a chairperson,
a secretary, and a treasurer can be selected from these 12 members.
2.
T
F
There are 360 different permutations of the letters “HOLLOW”
that can be made.
3.
T
F
A student must select five questions to answer from a choice of
eight questions. There are 40 ways this can be done.
4.
T
F
If seven objects are taken three at a time, there would be 140
combinations.
Show your work.
5.
A photographer wants to display 14 different photos. How many ways can this
be done?
6.
A photographer has 14 photos of 4 different models. Two are of model A, five
are of model B, four are of model C, and three are of model D. How many
distinguishable arrangements are possible?
7.
Different photographers entered 14 photos into a contest. How many ways can
1st, 2nd, and 3rd place be awarded?
8.
A photographer has 14 photos. He must choose 5 photos for display in the
gallery. How many ways can this be done?
9.
A photographer has 14 photos. Eight photos are of men and 6 photos are of
women. The photographer must choose a group of 3 men and 2 women for a
particular display. How many different possible groups can be formed?
10.
How many ways can 15 cards be arranged in a row?
11.
You have 20 cards: 6 clubs, 7 spades, 3 hearts, and 4 diamonds. How many
distinguishable ways (according to suit) can they be arranged in a row?
Elementary Statistics: Picturing the World - Prentice Hall
Created by Tina McRae for Ridge View High School
12.
If 20 people are playing poker. They earn prize money if they end up in the top
5 players. How many ways are there to determine 1st, 2nd, 3rd, 4th and 5th places
players?
13.
How many ways can 5 cards be selected from a standard deck of 52 cards?
14.
In a pile of 20 cards, you have 12 black and 8 red cards. How many ways can
your form a group of 3 black and 2 red cards from this pile?
Evaluate the following using your graphing calculator.
15.
5!
16.
7!
17.
1!
18.
10!
19.
5P5
20.
7P7
21.
5C5
22.
7C7
26.
50C25
Write the factorial fraction for the following.
23.
20P5
24.
50P25
25.
20C5
Elementary Statistics: Picturing the World - Prentice Hall
Created by Tina McRae for Ridge View High School
Probability Review
Probability & Counting Principles
Student _______________
Identify the sample space of the probability experiment.
1.
rolling one six-sided die
2.
tossing a coin two times
3.
determining the children’s gender for a family of three children (B or G)
Classify the statement as an example of theoretical probability, experimental
probability, or subjective probability. Circle your answer.
4.
T E S
The probability that it will rain tomorrow is 95%.
5.
T E S
The probability of picking a card and getting a black card is 50%.
6.
T E S
The probability that interest rates will rise during the summer is 0.05.
7.
T E S
The probability of winning the lottery is 1 in 10,000.
8.
T E S
The probability of a newborn baby being a boy is 0.5.
9.
T E S
The probability of passing this test is 85% based on your past
performance.
10.
Your coach wants you to give 110%. Explain why that is impossible.
Find the following theoretical probabilities. Show your fraction & decimal & %.
You roll two 6-sided dice.
11.
P(sum of 7) =
12.
P(doubles) =
13.
P(pair of evens) =
14.
P(sum greater than 5) =
You draw one card from a standard deck of cards.
15.
P(heart) =
16.
P(an even) =
17.
P(a face card) =
18.
P(a 2) =
Elementary Statistics: Picturing the World - Prentice Hall
Created by Tina McRae for Ridge View High School
A question has five multiple-choice answers.
19.
What is the probability of guessing the correct answer?
20.
What is the probability that you guess an incorrect answer?
I wrote down one number between 1 and 20.
21.
What is the probability that you randomly guess my number?
22.
What is the probability that you did not guess my number?
Students were asked to identify their favorite course in high school. The
results are shown in the following table. A student is chosen at random from
this group. Use the table to find the probability that his/her favorite class is…
23.
math
24.
history
25.
P.E.
26.
not Science
27.
not English
Class
Math
English
History
P.E.
Science
Frequency
98
65
76
87
54
Permutations & Combinations
Show how you obtain each answer.
28.
The access code to a security system consists of five digits (0 -9). How many
different codes are available if digits can be repeated?
29.
What is the probability of you walking up to a stranger’s security system and
randomly selecting the correct access code?
30.
The access code to a house’s security system consists of five digits. How many
different codes are available if the first digit cannot be zero?
31.
What is the probability of you walking up to this stranger’s security system and
randomly selecting the correct access code?
32.
A couple plans to have four kids. How many gender (B-G) sequences are possible?
33.
What is the probability that the couple has four boys?
Elementary Statistics: Picturing the World - Prentice Hall
Created by Tina McRae for Ridge View High School
34.
Each automobile license plate consists of a single digit (1 – 9) followed by three
letters, followed by three digits (1 – 9). How many different license plates can
be formed if the letter O is not allowed but there are no restrictions on
repeating digits or letters?
35.
A delivery route must include stops at 7 cities. How many different routes are
possible?
36.
What is the probability that the deliveries are made in “alphabetical” order
based on the city names?
37.
How many distinguishable permutations of the letters in the word
PROBABILITY are there?
38.
A couple has 5 kids – 3 boys and 2 girls. How many distinguishable gender
sequences are possible?
39.
How many ways can a jury of four men and four women be selected from twelve
men and ten women?
40.
In the lottery, you must select six numbers from fifty-two numbers to win the
big prize. The numbers do not have to be in a particular order. How many ways
are there to choose six numbers from fifty-two numbers?
41.
What is the probability that you will win the lottery if you buy one ticket?
42.
You are taking a 10-question true-false test. How many different ways are
there to answer the test?
43.
If you randomly answer the 10 questions without even reading the problems,
what is the probability that you will earn a 100 on the test?
44.
How many ways can 20 students be arranged in a list?
45.
What is the probability that the 20 students are randomly arranged and end up
in alphabetical order?
46.
How many ways can a group of 4 students be selected from a class of 20?
47.
Suzy is in this class. If she must be one of the group members, how many ways
can the group of 4 be selected from the class?
48.
What is the probability that Suzy will be randomly selected as one of the group
members?
Elementary Statistics: Picturing the World - Prentice Hall
Created by Tina McRae for Ridge View High School
49.
How many ways can a president, vice-president, secretary, and treasurer be
selected from a group of 20 students?
50.
Suzy is in this class. If she must be the secretary, how many ways can the
officers be selected from the class?
51.
What is the probability that Suzy will be randomly selected as one of the
officers?
52.
In a class of 20 students, there are 12 boys and 8 girls. How many ways can we
select a group of 5 boys and 2 girls?
Construct a tree diagram.
53.
At Moe’s you have some choices…
1) Burrito, Quesada, or Taco
2) Ground Beef or Chicken
3) Black beans or Pinto beans
54.
How many different options do you have?
55.
What is the probability of randomly choosing an option with chicken?
56.
What is the probability of randomly choosing an option that has beef and black
beans?
57.
What is the probability of randomly choosing a taco?
Elementary Statistics: Picturing the World - Prentice Hall
Created by Tina McRae for Ridge View High School