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Math Problems
Grade 8
Probability of independent and dependent events
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 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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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
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
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 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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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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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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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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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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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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In a certain Algebra
2
2
2
class of
29
29
29
students,
14
14
14
of them play basketball and
8
8
8
of them play baseball. There are
2
2
2
students who play both sports. What is the probability that a student chosen randomly from the class plays basketball or baseball?
\newline
Answer:
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In a certain Algebra
2
2
2
class of
30
30
30
students,
12
12
12
of them play basketball and
14
14
14
of them play baseball. There are
7
7
7
students who play neither sport. What is the probability that a student chosen randomly from the class plays both basketball and baseball?
\newline
Answer:
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In a certain Algebra
2
2
2
class of
23
23
23
students,
9
9
9
of them play basketball and
13
13
13
of them play baseball. There are
7
7
7
students who play both sports. What is the probability that a student chosen randomly from the class plays basketball or baseball?
\newline
Answer:
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In a certain Algebra
2
2
2
class of
22
22
22
students,
7
7
7
of them play basketball and
13
13
13
of them play baseball. There are
4
4
4
students who play both sports. What is the probability that a student chosen randomly from the class plays basketball or baseball?
\newline
Answer:
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In a certain Algebra
2
2
2
class of
29
29
29
students,
18
18
18
of them play basketball and
6
6
6
of them play baseball. There are
7
7
7
students who play neither sport. What is the probability that a student chosen randomly from the class plays both basketball and baseball?
\newline
Answer:
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In a certain Algebra
2
2
2
class of
30
30
30
students,
16
16
16
of them play basketball and
10
10
10
of them play baseball. There are
8
8
8
students who play neither sport. What is the probability that a student chosen randomly from the class plays basketball or baseball?
\newline
Answer:
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In a certain Algebra
2
2
2
class of
29
29
29
students,
9
9
9
of them play basketball and
15
15
15
of them play baseball. There are
11
11
11
students who play neither sport. What is the probability that a student chosen randomly from the class plays basketball or baseball?
\newline
Answer:
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In a math class with
24
24
24
students, a test was given the same day that an assignment was due. There were
15
15
15
students who passed the test and
17
17
17
students who completed the assignment. There were
4
4
4
students who failed the test and also did not complete the assignment. What is the probability that a student who did not complete the assignment passed the test?
\newline
Answer:
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In a class of
28
28
28
students,
7
7
7
play an instrument and
17
17
17
play a sport. There are
3
3
3
students who play an instrument and also play a sport. What is the probability that a student chosen randomly from the class plays a sport or an instrument?
\newline
Answer:
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In a class of
29
29
29
students,
12
12
12
play an instrument and
5
5
5
play a sport. There are
2
2
2
students who play an instrument and also play a sport. What is the probability that a student chosen randomly from the class does not play an instrument?
\newline
Answer:
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In a math class with
20
20
20
students, a test was given the same day that an assignment was due. There were
10
10
10
students who passed the test and
14
14
14
students who completed the assignment. There were
4
4
4
students who failed the test and also did not complete the assignment. What is the probability that a student passed the test given that they completed the assignment?
\newline
Answer:
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In a class of
30
30
30
students,
23
23
23
have a cat and
6
6
6
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 chosen randomly from the class has a cat?
\newline
Answer:
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In a class of
24
24
24
students,
6
6
6
are female and
12
12
12
have an
A
A
A
in the class. There are
4
4
4
students who are female and have an A in the class. What is the probability that a female student has an
A
\mathrm{A}
A
?
\newline
Answer:
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In a class of
27
27
27
students,
13
13
13
have a brother and
15
15
15
have a sister. There are
11
11
11
students who have a brother and a sister. What is the probability that a student who has a brother also has a sister?
\newline
Answer:
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In a class of
23
23
23
students,
11
11
11
play an instrument and
5
5
5
play a sport. There are
3
3
3
students who play an instrument and also play a sport. What is the probability that a student does not play an instrument given that they play a sport?
\newline
Answer:
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In a class of
23
23
23
students,
8
8
8
play an instrument and
13
13
13
play a sport. There are
4
4
4
students who do not play an instrument or a sport. What is the probability that a student who plays an instrument does not play a sport?
\newline
Answer:
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In a class of
30
30
30
students,
18
18
18
have a brother and
8
8
8
have a sister. There are
9
9
9
students who do not have any siblings. What is the probability that a student chosen randomly from the class does not have a brother?
\newline
Answer:
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In a class of
18
18
18
students,
8
8
8
have a cat and
7
7
7
have a dog. There are
3
3
3
students who have a cat and a dog. What is the probability that a student has a cat given that they do not have a dog?
\newline
Answer:
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In a class of
22
22
22
students,
9
9
9
play an instrument and
15
15
15
play a sport. There are
4
4
4
students who play an instrument and also play a sport. What is the probability that a student who plays an instrument also plays a sport?
\newline
Answer:
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In a math class with
19
19
19
students, a test was given the same day that an assignment was due. There were
12
12
12
students who passed the test and
13
13
13
students who completed the assignment. There were
4
4
4
students who failed the test and also did not complete the assignment. What is the probability that a student who completed the assignment passed the test?
\newline
Answer:
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