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Math Problems
Grade 8
Probability of independent and dependent events
A bag contains
2
2
2
orange balls and
3
3
3
blue balls. Two balls are selected without putting the first one back. What is the probability they are both orange?
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You flip a coin twice. What is the probability of getting tails and then getting heads? Write your answer as a percentage.
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In a class of
30
30
30
students,
18
18
18
have a cat and
21
21
21
have a dog. There are
5
5
5
students who do not have a cat or a dog. What is the probability that a student who has a dog also has a cat?
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You flip a coin twice. What is the probability of getting heads and then getting tails? Write your answer as a percentage.
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Section
A
A
A
of my math class has
110
110
110
students. Section
B
B
B
of my math class has
80
80
80
students. If I randomly select
15
15
15
students from the combined classes in a way that the order of my selection does not matter, what is the probability that all
15
15
15
students come from section
A
A
A
?
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You pick a card at random. Without putting the first card back, you pick a second card at random.
\newline
3456
3456
3456
\newline
What is the probability of picking a
6
6
6
and then picking a
6
6
6
?
\newline
Write your answer as a percentage.
\newline
_
_
_
_
%
\_\_\_\_\%
____%
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You pick a card at random. Without putting the first card back, you pick a second card at random.
\newline
1234
1234
1234
\newline
What is the probability of picking a
3
3
3
and then picking a
3
3
3
?
\newline
Write your answer as a percentage.
\newline
_
_
_
_
%
\_\_\_\_\%
____%
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You pick a card at random. Without putting the first card back, you pick a second card at random.
\newline
3456
3456
3456
\newline
What is the probability of picking a
6
6
6
and then picking a
6
6
6
?
\newline
Write your answer as a fraction or whole number.
\newline
_
_
_
_
\_\_\_\_
____
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At the first faculty meeting of the school year, Mifflin Middle School gives away prizes. This year, Mrs. Ramirez won a big basket of markers in assorted colors. She randomly picks one from the basket, notes its color, then puts it back. She does this
15
15
15
times and finds that she has picked
4
4
4
green,
3
3
3
pink, and
8
8
8
blue markers.
\newline
Based on the data, what is the probability of choosing a blue marker?
\newline
Write your answer as a fraction or whole number.
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Learn with an example
\newline
or
\newline
Watch a video
\newline
a video
\newline
0
0
0
(D)
\newline
A drawing class was assigned a final project where students had to choose one art medium and one genre. The professor kept track of the types of projects submitted.
\newline
\begin{tabular}{|l|c|c|}
\newline
\hline \multicolumn{
1
1
1
}{|c|}{} & Portrait & Landscape \\
\newline
\hline Acrylic paint &
8
8
8
&
2
2
2
\\
\newline
\hline Oil paint &
3
3
3
&
5
5
5
\\
\newline
\hline
\newline
\end{tabular}
\newline
What is the probability that a randomly selected student used oil paint and chose to create a landscape?
\newline
Simplify any fractions.
\newline
□
\square
□
\newline
Submit
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A spinner has
5
5
5
equally sized sections,
1
1
1
of which is gray and
4
4
4
of which are blue. The spinner is spun twice. What is the probability that the first spin lands on blue and the second spin lands on gray?
\newline
Write your answer as a fraction in simplest form.
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a bed of flowers consists of
100
100
100
stalks of flowers of which
20
20
20
are lillies,
h
h
h
are roses and the rest are tulips. given that the probability of picking a stalk of tulip at random is
1
4
\frac{1}{4}
4
1
find the value of
h
h
h
.
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JpQLsf
1
1
1
L-YB_a
4
4
4
YfDV
62
62
62
S
4
4
4
v_nDNXNTjtmsLGF
9
9
9
kPaWTXjVulMCOw/viewform?hr_submission=Chk
\newline
Question
7
7
7
*
\newline
A board game has two spinners. The first spinner has
4
4
4
equal areas labeled
1
1
1
,
2
2
2
,
3
3
3
and
4
4
4
. The second spinner has
3
3
3
equal areas that are labeled: Move Ahead, Move Back, and Do Not Move. What is the probability the first spinner will land on a
2
2
2
and the second spinner will NOT land on Move Back?
\newline
A
1
2
\frac{1}{2}
2
1
\newline
B
1
4
\frac{1}{4}
4
1
\newline
C
1
8
\frac{1}{8}
8
1
\newline
D
1
6
\frac{1}{6}
6
1
\newline
A
\newline
B
\newline
C
\newline
D
\newline
Question
8
8
8
\newline
7
7
7
. The list below snows the numbers of each type of music you nave on vour music playes.
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4
4
4
. If you spin the spinner twice, what is the probability of spinning pink then brown
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Three coins are simultaneously flipped, what is the probability that it lands exactly one head
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After growing tired of squinting while driving, Desmond went shopping for a pair of sunglasses. He tried on glasses with different frames and lenses.
\newline
\begin{tabular}{|l|c|c|c|}
\newline
\cline {
2
2
2
-
4
4
4
} & Cat eye frames & Browline frames & Aviator frames \\
\newline
\hline Polarized lenses &
2
2
2
&
8
8
8
&
7
7
7
\\
\newline
\hline Regular lenses &
7
7
7
&
4
4
4
&
8
8
8
\\
\newline
\hline
\newline
\end{tabular}
\newline
What is the probability that a randomly selected pair of sunglasses has cat eye frames and does not have regular lenses?
\newline
Simplify any fractions.
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Some sanitation workers sifted through some recycling and trash to see whether people had correctly sorted their plastic bottles.
\newline
\begin{tabular}{|l|c|c|c|}
\newline
\cline {
2
2
2
-
4
4
4
} & Plastic \#
2
2
2
& Plastic \#
4
4
4
& Plastic \#
5
5
5
\\
\newline
\hline Correctly placed &
5
5
5
&
7
7
7
&
7
7
7
\\
\newline
\hline Incorrectly placed &
6
6
6
&
5
5
5
&
5
5
5
\\
\newline
\hline
\newline
\end{tabular}
\newline
What is the probability that a randomly selected bottle is not correctly placed and is not made of plastic \#
2
2
2
?
\newline
Simplify any fractions.
\newline
□
\square
□
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Suzie is shopping for a new bicycle. She is most interested in color and type of tires.
\newline
\begin{tabular}{|l|c|c|}
\newline
\hline & Red & Green \\
\newline
\hline Road bike tires &
5
5
5
&
9
9
9
\\
\newline
\hline Mountain bike tires &
6
6
6
&
7
7
7
\\
\newline
\hline City bike tires &
8
8
8
&
7
7
7
\\
\newline
\hline
\newline
\end{tabular}
\newline
What is the probability that a randomly selected bike does not have mountain bike tires and is not red?
\newline
Simplify any fractions.
\newline
□
\square
□
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An online store sells a variety of photo albums. The albums range in photo capacity and orientation.
\newline
\begin{tabular}{|l|c|c|}
\newline
\hline & Horizontally & Vertically \\
\newline
\hline Under
50
50
50
photos &
5
5
5
&
4
4
4
\\
\newline
\hline
50
50
50
photos or more &
1
1
1
&
2
2
2
\\
\newline
\hline
\newline
\end{tabular}
\newline
What is the probability that a randomly selected photo album does not hold
50
50
50
photos or more or is not oriented vertically?
\newline
Simplify any fractions.
\newline
□
\square
□
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The owner of a sushi restaurant looked over some recent orders. He noted how many yellowtail and salmon rolls had been ordered.
\newline
\begin{tabular}{|l|c|c|}
\newline
\cline {
2
2
2
-
3
3
3
} & Not spicy & Spicy \\
\newline
\hline Yellowtail &
2
2
2
&
2
2
2
\\
\newline
\hline Salmon &
3
3
3
&
4
4
4
\\
\newline
\hline
\newline
\end{tabular}
\newline
What is the probability that a randomly selected sushi roll contains yellowtail and is not spicy?
\newline
Simplify any fractions.
\newline
□
\square
□
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Kamal likes to go on canoe trips, and on each trip he purchases oars to keep as souvenirs. His collection of oars is organized by decade and type of wood.
\newline
\begin{tabular}{|c|c|c|}
\newline
\hline & Spruce wood & Ash wood \\
\newline
\hline
2010
2010
2010
s &
2
2
2
&
2
2
2
\\
\newline
\hline
2020
2020
2020
s &
5
5
5
&
4
4
4
\\
\newline
\hline
\newline
\end{tabular}
\newline
What is the probability that a randomly selected oar was not purchased in the
2010
2010
2010
s and was not made from spruce wood?
\newline
Simplify any fractions.
\newline
□
\square
□
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Ken is a sandwich maker at a local deli. Last week, he tracked the number of peanut butter and jelly sandwiches ordered, noting the flavor of jelly and type of peanut butter requested.
\newline
\begin{tabular}{|l|c|c|}
\newline
\hline & Creamy peanut butter & Chunky peanut butter \\
\newline
\hline Strawberry jelly &
4
4
4
&
3
3
3
\\
\newline
\hline Grape jelly &
1
1
1
&
4
4
4
\\
\newline
\hline
\newline
\end{tabular}
\newline
What is the probability that a randomly selected sandwich was made with grape jelly or was not made with creamy peanut butter?
\newline
Simplify any fractions.
\newline
□
\square
□
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Over a weekend, Braden counted the number of single scoop ice creams ordered at his store. He tracked the flavors and the day on which it was ordered.
\newline
\begin{tabular}{|l|c|c|}
\newline
\cline {
2
2
2
-
3
3
3
} & Saturday & Sunday \\
\newline
\hline Chocolate &
6
6
6
&
1
1
1
\\
\newline
\hline Vanilla &
3
3
3
&
6
6
6
\\
\newline
\hline
\newline
\end{tabular}
\newline
What is the probability that a randomly selected ice cream was not vanilla and was not ordered on a Saturday?
\newline
Simplify any fractions.
\newline
□
\square
□
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If a fair die is rolled
6
6
6
times, what is the probability, to the nearest thousandth, of getting exactly
4
4
4
sixes?
\newline
Answer:
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If a fair die is rolled
3
3
3
times, what is the probability, to the nearest thousandth, of getting exactly
2
2
2
twos?
\newline
Answer:
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If a fair coin is tossed
5
5
5
times, what is the probability, to the nearest thousandth, of getting exactly
4
4
4
tails?
\newline
Answer:
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If a fair die is rolled
7
7
7
times, what is the probability, to the nearest thousandth, of getting exactly
1
1
1
two?
\newline
Answer:
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If a fair coin is tossed
4
4
4
times, what is the probability, rounded to the nearest thousandth, of getting at least
3
3
3
tails?
\newline
Answer:
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If a fair die is rolled
4
4
4
times, what is the probability, rounded to the nearest thousandth, of getting at least
3
3
3
fours?
\newline
Answer:
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If a fair die is rolled
4
4
4
times, what is the probability, rounded to the nearest thousandth, of getting at most
1
1
1
two?
\newline
Answer:
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If a fair coin is tossed
9
9
9
times, what is the probability, rounded to the nearest thousandth, of getting at least
8
8
8
tails?
\newline
Answer:
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If a fair die is rolled
5
5
5
times, what is the probability, rounded to the nearest thousandth, of getting at least
4
4
4
threes?
\newline
Answer:
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If a fair coin is tossed
5
5
5
times, what is the probability, rounded to the nearest thousandth, of getting at most
2
2
2
tails?
\newline
Answer:
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If a fair die is rolled
5
5
5
times, what is the probability, rounded to the nearest thousandth, of getting at most
1
1
1
four?
\newline
Answer:
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A bag contains
5
5
5
red marbles,
4
4
4
green marbles,
6
6
6
white marbles, and
5
5
5
black marbles. What is the probability of randomly drawing a red marble and then a green marble if the first marbled is replaced? Write your answer as a fraction in simplest form.
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In a particular school assembly of
120
120
120
students, there are
40
40
40
first graders,
20
20
20
of which are girls. If one student is chosen at random, what is the probability that the chosen student vill not be a first grade girl?
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A bag contains
6
6
6
red marbles,
7
7
7
blue marbles and
8
8
8
green marbles. If three marbles are drawn out of the bag, what is the exact probability that all three marbles drawn will be blue?
\newline
Answer:
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A bag contains
3
3
3
red marbles,
7
7
7
blue marbles and
8
8
8
green marbles. If three marbles are drawn out of the bag, what is the probability, to the nearest
1
1
1
oooth, that all three marbles drawn will be blue?
\newline
Answer:
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A bag contains
5
5
5
red marbles,
3
3
3
blue marbles and
6
6
6
green marbles. If two marbles are drawn out of the bag, what is the exact probability that both marbles drawn will be green?
\newline
Answer:
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A bag contains
5
5
5
red marbles,
4
4
4
blue marbles and
7
7
7
green marbles. If three marbles are drawn out of the bag, what is the exact probability that all three marbles drawn will be red?
\newline
Answer:
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A bag contains
5
5
5
red marbles,
8
8
8
blue marbles and
7
7
7
green marbles. If two marbles are drawn out of the bag, what is the exact probability that both marbles drawn will be blue?
\newline
Answer:
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A bag contains
2
2
2
red marbles,
5
5
5
blue marbles and
6
6
6
green marbles. If two marbles are drawn out of the bag, what is the exact probability that both marbles drawn will be green?
\newline
Answer:
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A bag contains
4
4
4
red marbles,
3
3
3
blue marbles and
7
7
7
green marbles. If two marbles are drawn out of the bag, what is the exact probability that both marbles drawn will be blue?
\newline
Answer:
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Adam invests money in an account paying a simple interest of
6
%
6 \%
6%
per year. If no money will be added or removed from the investment, what should he multiply his current balance by to find his total balance in a year in one step?
\newline
Answer:
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Riley owns a small business selling clothing. She knows that in the last week
88
88
88
customers paid cash,
17
17
17
customers used a debit card, and
3
3
3
customers used a credit card.
\newline
Based on these results, express the probability that the next customer will pay with cash as a percent to the nearest whole number.
\newline
Answer:
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Zoe owns a small business selling clothing. She knows that in the last week
41
41
41
customers paid cash,
54
54
54
customers used a debit card, and
44
44
44
customers used a credit card.
\newline
Based on these results, express the probability that the next customer will pay with a debit card as a fraction in simplest form.
\newline
Answer:
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13
13
13
. A store sells a box of highlighters that contains
4
4
4
yellow,
3
3
3
blue,
2
2
2
pink, and
1
1
1
green highlighter. What is the probability of randomly picking first
1
1
1
blue and then
1
1
1
pink highlighter from the box without replacing the blue highlighter?
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13
13
13
. At a school fair, the spinner represented in the accompanying diagram is spun twice. What is the probability that it will land in section
G
G
G
the first time and then in section
B
B
B
the second time?
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In a class of
6
6
6
, there are
2
2
2
students who forgot their lunch. If the teacher chooses
2
2
2
students, what is the probability that both of them forgot their lunch?
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A bag contains
6
6
6
red balls,
4
4
4
green balls, and
3
3
3
blue balls. If we choose a ball, then another ball without putting the first one back in the bag, what is the probability that the first ball will be green and the second will be red?
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1
2
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