Resources
Testimonials
Plans
Sign in
Sign up
Resources
Testimonials
Plans
Home
Math Problems
Algebra 2
Find probabilities using the binomial distribution
Mrs. Gomes found that
40
%
40 \%
40%
of students at her high school take chemistry. She randomly surveys
12
12
12
students. What is the probability that exactly
4
4
4
students have taken chemistry? Round the answer to the nearest thousandth.
Get tutor help
A certain insecticide kills
60
%
60\%
60%
of all insects in laboratory experiments. A sample of
12
12
12
insects is exposed to the insecticide in a particular experiment. What is the probability that exactly
10
10
10
insects will die?
Get tutor help
Last week, a flower delivery business conducted a survey on customer happiness. They found that
56
%
56\%
56%
of their customers were ＂pleased＂ with the service.
\newline
If the company surveys
4
4
4
of their customers the next week, what is the probability that exactly
1
1
1
is pleased?
\newline
Write your answer as a decimal rounded to the nearest thousandth.
\newline
____
\newline
Get tutor help
A surfboard factory just discovered a manufacturing error that causes some of the surfboards to crack easily. As a result, the factory recalled all of the surfboards sold in the last year. Each surfboard has a
75
%
75\%
75%
chance of having the defect.
\newline
If the factory recalled
3
3
3
surfboards, what is the probability that
0
0
0
of the boards have the defect?
\newline
Write your answer as a decimal rounded to the nearest thousandth.
\newline
____
\newline
Get tutor help
Last week, a flower delivery business conducted a survey on customer happiness. They found that
30
%
30\%
30%
of their customers were ＂pleased＂ with the service.
\newline
If the company surveys
2
2
2
of their customers the next week, what is the probability that
0
0
0
are pleased?
\newline
Write your answer as a decimal rounded to the nearest thousandth.
\newline
____
\newline
Get tutor help
Naomi and her teammates are each chewing a piece of tropical flavored gum before their championship softball game.
85
%
85\%
85%
of the pieces are pineapple flavored.
\newline
If
4
4
4
of her teammates are chosen at random, what is the probability that
0
0
0
are chewing pineapple gum?
\newline
Write your answer as a decimal rounded to the nearest thousandth.
\newline
____
\newline
Get tutor help
Sophia and her teammates are each chewing a piece of tropical flavored gum before their championship softball game.
58
%
58\%
58%
of the pieces are pineapple flavored.
\newline
If
2
2
2
of her teammates are chosen at random, what is the probability that exactly
2
2
2
are chewing pineapple gum?
\newline
Write your answer as a decimal rounded to the nearest thousandth.
\newline
____
\newline
Get tutor help
This Friday, Patty has a French vocabulary test as well as a Spanish vocabulary test. To prepare, she made a study card for each word,
42
%
42\%
42%
of which are French. Every time she picks a card, she sticks it back in the deck and shuffles again.
\newline
If Patty picks a study card from the deck
5
5
5
times during her first study session, what is the probability that exactly
4
4
4
cards have a French word?
\newline
Write your answer as a decimal rounded to the nearest thousandth.
\newline
____
\newline
Get tutor help
A social media company holds weekly meetings, which all employees are required to attend. At these meetings, the head of the company randomly selects employees to share an accomplishment from the past week.
21
%
21\%
21%
of company employees work in the marketing department.
\newline
If the head of the company randomly chooses
4
4
4
employees to share accomplishments at the next meeting, what is the probability that
0
0
0
employees work in the marketing department?
\newline
Write your answer as a decimal rounded to the nearest thousandth.
\newline
____
Get tutor help
Colleen and her teammates are each chewing a piece of tropical flavored gum before their championship softball game.
40
%
40\%
40%
of the pieces are pineapple flavored. If
2
2
2
of her teammates are chosen at random, what is the probability that
0
0
0
are chewing pineapple gum? Write your answer as a decimal rounded to the nearest thousandth. ____
Get tutor help
19
%
19\%
19%
of students in a class have black hair. If
4
4
4
students are chosen at random, what is the probability that
0
0
0
have black hair? Write your answer as a decimal rounded to the nearest thousandth. ____
Get tutor help
Greta and her teammates are each chewing a piece of tropical flavored gum before their championship softball game.
48
%
48\%
48%
of the pieces are pineapple flavored.
\newline
If
3
3
3
of her teammates are chosen at random, what is the probability that exactly
1
1
1
is chewing pineapple gum?
\newline
Write your answer as a decimal rounded to the nearest thousandth.
\newline
____
\newline
Get tutor help
Bernard read an article that claimed
38
%
38\%
38%
of students majoring in Political Science plan to go to law school. Curious about the claim, Bernard surveyed some of his Political Science classmates about their career goals. If the article's claim is true, and Bernard surveyed
5
5
5
classmates, what is the probability that
0
0
0
plan to go to law school? Write your answer as a decimal rounded to the nearest thousandth.____
Get tutor help
The founders of an online dating website believe there is a
61
%
61\%
61%
chance that a user believes in love at first sight. If
5
5
5
of the website's users are randomly selected to participate in a speed dating event, what is the probability that exactly
5
5
5
of them believe in love at first sight? Write your answer as a decimal rounded to the nearest thousandth.____
Get tutor help
Maura created her own deck of cards for a magic trick. She decorated all the cards with pictures of her family members.
16
%
16\%
16%
of the cards contained pictures of her brother. If Maura draws a random card from the deck
2
2
2
times, what is the probability that exactly
1
1
1
of the cards has a picture of Maura's brother? Write your answer as a decimal rounded to the nearest thousandth.____
Get tutor help
A health psychologist was researching the role of choice in food consumption. In one experiment, the psychologist offered a group of children a choice of either a chocolate chip cookie or fresh fruit. Earlier results indicate that
63
%
63\%
63%
of children choose the chocolate chip cookie. If the earlier results are accurate, and the psychologist randomly picks
4
4
4
children to interview after the experiment, what is the probability that exactly
2
2
2
of the children chose the chocolate chip cookies? Write your answer as a decimal rounded to the nearest thousandth____.
Get tutor help
A recent school survey found that
31
%
31\%
31%
of Sasha's classmates speak at least two languages. If
3
3
3
of her classmates are chosen at random, what is the probability that
0
0
0
speak at least two languages? Write your answer as a decimal rounded to the nearest thousandth.____
Get tutor help
A psychology professor surveyed her class and determined that
59
%
59\%
59%
of the students have acrophobia, a fear of heights. If
2
2
2
of the students are chosen at random, what is the probability that
0
0
0
have acrophobia?
\newline
Write your answer as a decimal rounded to the nearest thousandth.____
Get tutor help
A biomedical engineering professor warned her students that their upcoming exam would contain some questions from previous exams. Each question from a previous test has a
13
%
13\%
13%
chance of being on the upcoming exam.
\newline
If a student studies
3
3
3
previous exam questions, what is the probability that exactly
2
2
2
of the questions will be on the upcoming exam?
\newline
Write your answer as a decimal rounded to the nearest thousandth.____
Get tutor help
Lauren created her own deck of cards for a magic trick. She decorated all the cards with pictures of her family members.
12
%
12\%
12%
of the cards contained pictures of her brother.
\newline
If Lauren draws a random card from the deck
2
2
2
times, what is the probability that exactly
2
2
2
of the cards have a picture of Lauren's brother?
\newline
Write your answer as a decimal rounded to the nearest thousandth.
\newline
____
\newline
Get tutor help
Xavier wrote a short fiction story about a tiny world where
76
%
76\%
76%
of inhabitants have a gene that allows them to breathe underwater. If
5
5
5
inhabitants are randomly chosen to be tested for the gene, what is the probability that exactly
2
2
2
have the gene? Write your answer as a decimal rounded to the nearest thousandth. ____
Get tutor help
Tammy hosts a trivia night at her house every Thursday. She generates questions using a trivia website. The website claims that there is a
29
%
29\%
29%
chance that a generated question is a history question.
\newline
If the claim is correct, and Tammy randomly generates
5
5
5
questions during the first round of trivia, what is the probability that exactly
1
1
1
will be a history question?
\newline
Write your answer as a decimal rounded to the nearest thousandth.
\newline
____
\newline
Get tutor help
Finn bought new equipment for his bowling alley, including a ball return machine. There is a
51
%
51\%
51%
chance that the machine returns a bowling ball with the finger holes facing up.
\newline
If the machine returns
3
3
3
bowling balls, what is the probability that exactly
1
1
1
ball will have the finger holes facing up?
\newline
Write your answer as a decimal rounded to the nearest thousandth.
\newline
____
\newline
Get tutor help
Todd bought new equipment for his bowling alley, including a ball return machine. There is a
66
%
66\%
66%
chance that the machine returns a bowling ball with the finger holes facing up.
\newline
If the machine returns
3
3
3
bowling balls, what is the probability that exactly
2
2
2
will have the finger holes facing up?
\newline
Write your answer as a decimal rounded to the nearest thousandth.
\newline
____
\newline
Get tutor help
This Friday, Eva has a French vocabulary test as well as a Spanish vocabulary test. To prepare, she made a study card for each word,
40
%
40\%
40%
of which are French. Every time she picks a card, she sticks it back in the deck and shuffles again.
\newline
If Eva picks a study card from the deck
4
4
4
times during her first study session, what is the probability that exactly
4
4
4
cards have a French word?
\newline
Write your answer as a decimal rounded to the nearest thousandth.
\newline
____
\newline
Get tutor help
A biomedical engineering professor warned her students that their upcoming exam would contain some questions from previous exams. Each question from a previous test has a
14
%
14\%
14%
chance of being on the upcoming exam.
\newline
If a student studies
3
3
3
previous exam questions, what is the probability that exactly
3
3
3
of the questions will be on the upcoming exam?
\newline
Write your answer as a decimal rounded to the nearest thousandth.
\newline
____
\newline
Get tutor help
It is believed that
71
%
71\%
71%
of tickets purchased for an upcoming music festival are actually legitimate tickets. The rest are fake tickets sold by scam artists. Assume everyone who bought a ticket shows up at the concert.
\newline
If security guards at the festival randomly select
4
4
4
tickets to examine in more detail, what is the probability that exactly
1
1
1
of those tickets is legitimate?
\newline
Write your answer as a decimal rounded to the nearest thousandth.
\newline
____
\newline
Get tutor help
A social media company holds weekly meetings, which all employees are required to attend. At these meetings, the head of the company randomly selects employees to share an accomplishment from the past week.
20
%
20\%
20%
of company employees work in the marketing department.
\newline
If the head of the company randomly chooses
4
4
4
employees to share accomplishments at the next meeting, what is the probability that exactly
2
2
2
employees work in the marketing department?
\newline
Write your answer as a decimal rounded to the nearest thousandth.
\newline
____
\newline
Get tutor help
78
%
78\%
78%
of cows on a farm are pregnant. If
5
5
5
cows are chosen at random, what is the probability that exactly
3
3
3
are pregnant? Write your answer as a decimal rounded to the nearest thousandth. ____
Get tutor help
Addison is a physical therapist who specializes in pediatric leg injuries. Her patients differ in age and type of injury.
\newline
\begin{tabular}{|l|c|c|}
\newline
\hline & Knee pain & Ankle pain \\
\newline
\hline
0
−
12
0-12
0
−
12
years old &
3
3
3
&
6
6
6
\\
\newline
\hline
13
−
19
13-19
13
−
19
years old &
4
4
4
&
5
5
5
\\
\newline
\hline
\newline
\end{tabular}
\newline
What is the probability that a randomly selected patient is not
13
−
19
13-19
13
−
19
years old and does not suffer from ankle pain?
\newline
Simplify any fractions.
\newline
□
\square
□
Get tutor help
4
4
4
. A builder is covering the floor of a rectangular room that is
23
23
23
feet by
25
25
25
feet with tiles that are
1
1
1
foot by
1
1
1
foot. The tiles are sold in boxes of
12
12
12
.
\newline
Diego says
59
59
59
boxes are needed to cover the floor, and that there will be a few leftover tiles.
\newline
a. Is Diego's answer reasonable? Explain or show your reasoning.
Get tutor help
If the probability that the Islanders will beat the Rangers in a game is
61
%
61 \%
61%
, what is the probability that the Islanders will win exactly five out of seven games in a series against the Rangers? Round your answer to the nearest thousandth.
\newline
Answer:
Get tutor help
Mr. and Mrs. Doran have a genetic history such that the probability that a child being born to them with a certain trait is
63
%
63 \%
63%
. If they have three children, what is the probability that exactly two of their three children will have that trait? Round your answer to the nearest thousandth.
\newline
Answer:
Get tutor help
If the probability that the Islanders will beat the Rangers in a game is
18
%
18 \%
18%
, what is the probability that the Islanders will win exactly one out of six games in a series against the Rangers? Round your answer to the nearest thousandth.
\newline
Answer:
Get tutor help
Mr. and Mrs. Doran have a genetic history such that the probability that a child being born to them with a certain trait is
0
0
0
.
89
89
89
. If they have five children, what is the probability that exactly five of their five children will have that trait? Round your answer to the nearest thousandth.
\newline
Answer:
Get tutor help
Mr. and Mrs. Doran have a genetic history such that the probability that a child being born to them with a certain trait is
44
%
44 \%
44%
. If they have three children, what is the probability that exactly one of their three children will have that trait? Round your answer to the nearest thousandth.
\newline
Answer:
Get tutor help
Mr. and Mrs. Doran have a genetic history such that the probability that a child being born to them with a certain trait is
2
/
3
2 / 3
2/3
. If they have five children, what is the probability that at least four of their five children will have that trait? Round your answer to the nearest thousandth.
\newline
Answer:
Get tutor help
Mr. and Mrs. Doran have a genetic history such that the probability that a child being born to them with a certain trait is
2
/
3
2 / 3
2/3
. If they have five children, what is the probability that at most two of their five children will have that trait? Round your answer to the nearest thousandth.
\newline
Answer:
Get tutor help
Mr. and Mrs. Doran have a genetic history such that the probability that a child being born to them with a certain trait is
0
0
0
.
41
41
41
. If they have six children, what is the probability that at least four of their six children will have that trait? Round your answer to the nearest thousandth.
\newline
Answer:
Get tutor help
Mr. and Mrs. Doran have a genetic history such that the probability that a child being born to them with a certain trait is
41
%
41 \%
41%
. If they have four children, what is the probability that at most one of their four children will have that trait? Round your answer to the nearest thousandth.
\newline
Answer:
Get tutor help
Mr. and Mrs. Doran have a genetic history such that the probability that a child being born to them with a certain trait is
69
%
69 \%
69%
. If they have five children, what is the probability that at most one of their five children will have that trait? Round your answer to the nearest thousandth.
\newline
Answer:
Get tutor help
If the probability that the Islanders will beat the Rangers in a game is
0
0
0
.
71
71
71
, what is the probability that the Islanders will win at most two out of seven games in a series against the Rangers? Round your answer to the nearest thousandth.
\newline
Answer:
Get tutor help
The Hiking Club plans to go camping in a State park where the probability of rain on any given day is
11
%
11 \%
11%
. What is the probability that it will rain on at most one of the six days they are there? Round your answer to the nearest thousandth.
\newline
Answer:
Get tutor help
QUESTION
5
5
5
\newline
A nutritionist is studying the servings of vegetables their patients consume each day. It is known that the average amount of vegetable servings consumed by an adult per day is
2
2
2
.
7
7
7
servings. After talking to their patients, the nutritionist believes the average amount of vegetable servings is different.
\newline
What are the hypotheses?
\newline
Fill in the blanks with the correct symbol
(
=
,
≠
,
<
(=, \neq,<
(
=
,
=
,
<
, or
>
)
>)
>
)
to repiesent the correct hypothesis.
\newline
Provide your answer below:
Get tutor help
Through ten games of basketball this season, Tyler has made
6
%
6 \%
6%
of his free-throws. Which word or phrase describes the probability that Tyler will hit his next free throw?
\newline
unlikely
\newline
certain
\newline
impossible
\newline
an equal chance or
50
50
50
−
50
-50
−
50
Get tutor help
The weather forecaster says that tomorrow there is a
92
%
92 \%
92%
chance that it will rain. Which word or phrase describes the probability that it will rain?
\newline
likely
\newline
impossible
\newline
unlikely
\newline
an equal chance or
50
50
50
−
50
-50
−
50
Get tutor help
The table shows the distribution, by age and gender, of the
30
30
30
.
0
0
0
million people in a certain region who live alone. Use the data in the table to find the probability that a randomly selected person in the region is a woman in the
18
18
18
−
24
-24
−
24
age range living alone.
\newline
\begin{tabular}{|l|c|c|c|c|c|c|c|}
\newline
\hline & \begin{tabular}{l}
\newline
Ages \\
\newline
18
−
24
18-24
18
−
24
\newline
\end{tabular} & \begin{tabular}{l}
\newline
Ages \\
\newline
25
−
34
25-34
25
−
34
\newline
\end{tabular} & \begin{tabular}{l}
\newline
Ages \\
\newline
35
−
44
35-44
35
−
44
\newline
\end{tabular} & \begin{tabular}{l}
\newline
Ages \\
\newline
45
−
64
\mathbf{4 5 - 6 4}
45
−
64
\newline
\end{tabular} & \begin{tabular}{l}
\newline
Ages \\
\newline
65
−
74
65-\mathbf{7 4}
65
−
74
\newline
\end{tabular} & \begin{tabular}{l}
\newline
Ages \\
\newline
275
\mathbf{2 7 5}
275
\newline
\end{tabular} & \\
\newline
\cline {
1
1
1
-
7
7
7
} Man &
0
0
0
.
6
6
6
&
2
2
2
.
4
4
4
&
2
2
2
.
3
3
3
&
4
4
4
.
3
3
3
&
1
1
1
.
5
5
5
&
1
1
1
.
2
2
2
&
12
12
12
.
3
3
3
\\
\newline
\hline Woman &
0
0
0
.
7
7
7
&
1
1
1
.
3
3
3
&
1
1
1
.
8
8
8
&
6
6
6
.
0
0
0
&
2
2
2
.
8
8
8
&
5
5
5
.
1
1
1
&
17
17
17
.
7
7
7
\\
\newline
\hline Total &
1
1
1
.
3
3
3
&
3
3
3
.
7
7
7
&
4
4
4
.
1
1
1
&
10
10
10
.
3
3
3
&
4
4
4
.
3
3
3
&
6
6
6
.
3
3
3
&
30
30
30
.
0
0
0
\\
\newline
\hline
\newline
\end{tabular}
\newline
The probability is
□
\square
□
.
\newline
(Type an integer or decimal rounded to the nearest hundredth as needed.)
Get tutor help
A restaurant server claims that \(28\)% of the time he leaves candy with the bill, the customer tips well.
\newline
If the server's claim is true, and one day he leaves candy with \(4\) customers' bills, what is the probability that exactly \(3\) of those customers will tip well?
\newline
Write your answer as a decimal rounded to the nearest thousandth.
Get tutor help
