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Find probabilities using the binomial distribution

Mr. Carter is planning a special event for

98

guests. A catering company tells him that the cost of food for each guest will be

\$16

. The cost for drinks for each guest will be another

\$5

. Based on that, Mr. Carter works out that the total catering bill will be

20,580

\$

. Does that sound about right?

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(B) No, it is much too high.

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(C) No, it is much too low.

Mrs. Gomes found that

40 \%

of students at her high school take chemistry. She randomly surveys

12

students. What is the probability that exactly

4

students have taken chemistry? Round the answer to the nearest thousandth.

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\%

chance of having the defect.

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If the factory recalled

3

surfboards, what is the probability that

0

of the boards have the defect?

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Write your answer as a decimal rounded to the nearest thousandth.

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Last week, a flower delivery business conducted a survey on customer happiness. They found that

56\%

of their customers were ＂pleased＂ with the service.

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If the company surveys

4

of their customers the next week, what is the probability that exactly

1

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Write your answer as a decimal rounded to the nearest thousandth.

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Last week, a flower delivery business conducted a survey on customer happiness. They found that

30\%

of their customers were ＂pleased＂ with the service.

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If the company surveys

2

of their customers the next week, what is the probability that

0

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Write your answer as a decimal rounded to the nearest thousandth.

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Naomi and her teammates are each chewing a piece of tropical flavored gum before their championship softball game.

85\%

of the pieces are pineapple flavored.

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4

of her teammates are chosen at random, what is the probability that

0

are chewing pineapple gum?

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Write your answer as a decimal rounded to the nearest thousandth.

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Sophia and her teammates are each chewing a piece of tropical flavored gum before their championship softball game.

58\%

of the pieces are pineapple flavored.

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2

of her teammates are chosen at random, what is the probability that exactly

2

are chewing pineapple gum?

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Write your answer as a decimal rounded to the nearest thousandth.

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Greta and her teammates are each chewing a piece of tropical flavored gum before their championship softball game.

48\%

of the pieces are pineapple flavored.

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3

of her teammates are chosen at random, what is the probability that exactly

1

is chewing pineapple gum?

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Write your answer as a decimal rounded to the nearest thousandth.

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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\%

of which are French. Every time she picks a card, she sticks it back in the deck and shuffles again.

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If Patty picks a study card from the deck

5

times during her first study session, what is the probability that exactly

4

cards have a French word?

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Write your answer as a decimal rounded to the nearest thousandth.

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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\%

of company employees work in the marketing department.

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If the head of the company randomly chooses

4

employees to share accomplishments at the next meeting, what is the probability that

0

employees work in the marketing department?

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Write your answer as a decimal rounded to the nearest thousandth.

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Colleen and her teammates are each chewing a piece of tropical flavored gum before their championship softball game.

40\%

of the pieces are pineapple flavored. If

2

of her teammates are chosen at random, what is the probability that

0

are chewing pineapple gum? Write your answer as a decimal rounded to the nearest thousandth. ____

19\%

of students in a class have black hair. If

4

students are chosen at random, what is the probability that

0

have black hair? Write your answer as a decimal rounded to the nearest thousandth. ____

The founders of an online dating website believe there is a

61\%

chance that a user believes in love at first sight. If

5

of the website's users are randomly selected to participate in a speed dating event, what is the probability that exactly

5

of them believe in love at first sight? Write your answer as a decimal rounded to the nearest thousandth.____

Finn bought new equipment for his bowling alley, including a ball return machine. There is a

51\%

chance that the machine returns a bowling ball with the finger holes facing up.

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If the machine returns

3

bowling balls, what is the probability that exactly

1

ball will have the finger holes facing up?

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Write your answer as a decimal rounded to the nearest thousandth.

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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\%

chance that a generated question is a history question.

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If the claim is correct, and Tammy randomly generates

5

questions during the first round of trivia, what is the probability that exactly

1

will be a history question?

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Write your answer as a decimal rounded to the nearest thousandth.

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Xavier wrote a short fiction story about a tiny world where

76\%

of inhabitants have a gene that allows them to breathe underwater. If

5

inhabitants are randomly chosen to be tested for the gene, what is the probability that exactly

2

have the gene? Write your answer as a decimal rounded to the nearest thousandth. ____

Lauren created her own deck of cards for a magic trick. She decorated all the cards with pictures of her family members.

12\%

of the cards contained pictures of her brother.

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If Lauren draws a random card from the deck

2

times, what is the probability that exactly

2

of the cards have a picture of Lauren's brother?

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Write your answer as a decimal rounded to the nearest thousandth.

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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\%

chance of being on the upcoming exam.

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If a student studies

3

previous exam questions, what is the probability that exactly

2

of the questions will be on the upcoming exam?

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Write your answer as a decimal rounded to the nearest thousandth.____

A psychology professor surveyed her class and determined that

59\%

of the students have acrophobia, a fear of heights. If

2

of the students are chosen at random, what is the probability that

0

have acrophobia?

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Write your answer as a decimal rounded to the nearest thousandth.____

A recent school survey found that

31\%

of Sasha's classmates speak at least two languages. If

3

of her classmates are chosen at random, what is the probability that

0

speak at least two languages? Write your answer as a decimal rounded to the nearest thousandth.____

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\%

of children choose the chocolate chip cookie. If the earlier results are accurate, and the psychologist randomly picks

4

children to interview after the experiment, what is the probability that exactly

2

of the children chose the chocolate chip cookies? Write your answer as a decimal rounded to the nearest thousandth____.

Maura created her own deck of cards for a magic trick. She decorated all the cards with pictures of her family members.

16\%

of the cards contained pictures of her brother. If Maura draws a random card from the deck

2

times, what is the probability that exactly

1

of the cards has a picture of Maura's brother? Write your answer as a decimal rounded to the nearest thousandth.____

Bernard read an article that claimed

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

classmates, what is the probability that

0

plan to go to law school? Write your answer as a decimal rounded to the nearest thousandth.____

Todd bought new equipment for his bowling alley, including a ball return machine. There is a

66\%

chance that the machine returns a bowling ball with the finger holes facing up.

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If the machine returns

3

bowling balls, what is the probability that exactly

2

will have the finger holes facing up?

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Write your answer as a decimal rounded to the nearest thousandth.

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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\%

of which are French. Every time she picks a card, she sticks it back in the deck and shuffles again.

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If Eva picks a study card from the deck

4

times during her first study session, what is the probability that exactly

4

cards have a French word?

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Write your answer as a decimal rounded to the nearest thousandth.

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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\%

chance of being on the upcoming exam.

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If a student studies

3

previous exam questions, what is the probability that exactly

3

of the questions will be on the upcoming exam?

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Write your answer as a decimal rounded to the nearest thousandth.

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It is believed that

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.

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If security guards at the festival randomly select

4

tickets to examine in more detail, what is the probability that exactly

1

of those tickets is legitimate?

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Write your answer as a decimal rounded to the nearest thousandth.

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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\%

of company employees work in the marketing department.

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If the head of the company randomly chooses

4

employees to share accomplishments at the next meeting, what is the probability that exactly

2

employees work in the marketing department?

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Write your answer as a decimal rounded to the nearest thousandth.

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78\%

of cows on a farm are pregnant. If

5

cows are chosen at random, what is the probability that exactly

3

are pregnant? Write your answer as a decimal rounded to the nearest thousandth. ____

If the probability that the Islanders will beat the Rangers in a game is

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.

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If the probability that the Islanders will beat the Rangers in a game is

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.

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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 \%

. 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.

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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

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.

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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 \%

. 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.

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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

. 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.

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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

. 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.

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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

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.

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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 \%

. 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.

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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 \%

. 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.

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If the probability that the Islanders will beat the Rangers in a game is

0

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.

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The Hiking Club plans to go camping in a State park where the probability of rain on any given day is

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.

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Through ten games of basketball this season, Tyler has made

6 \%

of his free-throws. Which word or phrase describes the probability that Tyler will hit his next free throw?

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an equal chance or

50

-50

The weather forecaster says that tomorrow there is a

92 \%

chance that it will rain. Which word or phrase describes the probability that it will rain?

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an equal chance or

50

-50

A restaurant server claims that \(28\)% of the time he leaves candy with the bill, the customer tips well.

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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?

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Write your answer as a decimal rounded to the nearest thousandth.