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Find probabilities using the binomial distribution

Grayson surveyed some students at his school about their favorite colors. Of the students surveyed,

2

said orange was their favorite color, while

36

of the students had other favorite colors. What is the experimental probability that the next student Grayson talks to will pick orange?

I start with an

\mathrm{N}

and end with an

\mathrm{A}

, a celestial beauty, far away. A stellar nursery, where stars are born, in the night sky, I adorn. I'm a cloud of dust and gas, through a telescope, don't let me pass. From the Eagle to the Horsehead, I wear many masks, capturing the universe's tasks. Who am I, this celestial drape, painting the cosmos, in vibrant shape?

The winter clothing drive has received donations of

c

g

pairs of gloves,

s

h

hats so far. Based on this data, what is a reasonable estimate of the probability that the next donation is not a pair of gloves?

The winter clothing drive has received donations of

c

g

pairs of gloves,

s

h

hats so far. Based on this data, what is a reasonable estimate of the probability that the next donation is not a pair of gloves?

Bert and Duncan take long walks every evening. Bert walks at a constant speed of

4\,\text{kilometers per hour}

, and Duncan walks at a constant speed of

5\,\text{kilometers per hour}

. One evening, Bert headed out first, and had already gone

2\,\text{kilometers}

when Duncan started his walk. How long after Duncan started his walk will they have walked the same distance?

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Write a system of equations, graph them, and type the solution.

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\_\_\_\_

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Zendaya recorded the grade-level and instrument of everyone in the middle school School of Rock below. Seventh Grade Students Instrument # of Students Guitar

7

15

12

6

Eighth Grade Students Instrument # of Students Guitar

7

13

8

12

Based on these results, express the probability that an eighth grader chosen at random will play the drums as a percent to the nearest whole number.

Camila owns a small business selling used books. She knows that in the last week

40

customers paid cash,

16

customers used a debit card, and

39

customers used a credit card. Based on these results, express the probability that the next customer will pay with a credit card as a decimal to the nearest hundredth.

A spinner is divided into five colored sections that are not of equal size: red, blue, green, yellow, and purple. The spinner is spun several times, and the results are recorded below: Spinner Results Color

\quad

\quad

2

\quad

11

\quad

5

\quad

11

\quad

\quad

0

Based on these results, express the probability that the next spin will land on blue or green or purple as a percent to the nearest whole number.

Elijah's scout troop took a field trip to the local fire station. They learned that Benjamin Franklin established the first volunteer fire company in

1736

! At the end of the trip, the scouts spun a spinner to determine what color fire helmet each got to take home. Here are the spinner results of the scouts who spun before Elijah:

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red, yellow, blue, yellow, green, yellow, red, blue, green, red, yellow, blue, yellow, green

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Based on the data, what is the probability of the spinner landing on red during Elijah's turn?

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Write your answer as a fraction or whole number.

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Leslie used some of her allowance money to buy a stack of

300

baseball trading cards at a yard sale. She randomly looks at

24

8

7

4

5

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Based on the data, what is the probability that the next card Leslie looks at will be a pitcher?

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Write your answer as a fraction or whole number.

Sally's investment of

\$7980

earns interest at

5\%

per year. compounded quarterly over

7

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What is the amount of interest earned?

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Write your answer to the nearest cent.

p(t)=100\left(\dfrac{1}{2}\right)^{\dfrac{t}{8.02}}

Radioactive isotopes are unstable atoms that decay into other atoms. Iodine

-131

is a radioactive isotope. The function models

p

, the percentage of iodine

-131

atoms remaining in a sample after

t

days. To the nearest tenth of a percent, what percent of iodine

-131

atoms remain in the sample after

10

An ordinary (fair) die is a cube with the numbers

1

6

on the sides (represented by painted spots). Imagine that such a die is rolled twice in succession and that the face values of the two rolls are added together. This sum is recorded as the outcome of a single trial of a random experiment.

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Compute the probability of each of the following events.

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A

: The sum is greater than

8

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B

: The sum is an odd number.

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Write your answers as fractions.

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P(A)=

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P(B)=

The gestation time of humans has an approximate Normal distribution with a mean of

250

days and a standard deviatim-

6

0

days. A simple random sample of

n

newborns is to be taken.

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What is the minimum sample sized needed so that the sampling distribution of

\bar{x}

has a standard deviation of

0

5

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15

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144

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12

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250

20\%

of newborns are born more than

1

week before their due date. A random sample of

20

newborns is selected.

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The standard deviation of the sampling distribution for the proportion of your sample that is born more than

7

days before their due date is

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0.20

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3.2

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0.089

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0.008

A random sample of

200

students was asked to sample a new type of pizza that the school was considering using as a replacement for the current pizza. Each student stated if they were a freshman, sophomore, junior, or senior and also if they liked the new pizza more than the current pizza (or not). The school would like to know if there is a relationship between grade level and pizza opinion.

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

86\%

of the pieces are pineapple flavored.

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3

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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Last year, Melissa came in

2

nd place in her school's Spelling Bee. This year, she plans to win

1

st place. She compiled a long list of words to study,

49\%

of which have a Latin root.

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If Melissa randomly chooses a word to study from the list

5

different times this month, what is the probability that exactly

2

of the words have a Latin root?

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

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This Friday, Tucker has a French vocabulary test as well as a Spanish vocabulary test. To prepare, he made a study card for each word,

44\%

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

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If Tucker picks a study card from the deck

5

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

3

cards have a French word?

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

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Some friends are taking turns spinning a toy to see how it lands. The toy has four sides, each with a different animal displayed. The toy is weighted unevenly, so that it lands on the turtle

21\%

of the time. If one of the friends spins the toy

2

times, what is the probability that it lands on the turtle exactly

2

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

56\%

of students in a class have black hair. If

5

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

2

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

Last year, Khalil came in

2

nd place in his school's Spelling Bee. This year, he plans to win

1

st place. He compiled a long list of words to study,

51\%

of which have a Latin root.

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If Khalil randomly chooses a word to study from the list

2

different times this month, what is the probability that

0

of the words have a Latin root?

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

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Braden 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. If the machine returns

5

bowling balls, what is the probability that exactly

4

will have the finger holes facing up? Write your answer as a decimal rounded to the nearest thousandth. ____

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

5

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

4

of the tickets are legitimate?

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

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An art museum recently discovered that

19\%

of their paintings had been stolen and replaced with replicas. If a tourist observes

2

different paintings at random, what is the probability that exactly

1

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

Last year, Ashley came in

2

nd place in her school's Spelling Bee. This year, she plans to win

1

st place. She compiled a long list of words to study,

23\%

of which have a Latin root.

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If Ashley randomly chooses a word to study from the list

5

different times this month, what is the probability that exactly

3

of the words have a Latin root?

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

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65\%

of cows on a farm are pregnant.

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2

cows are chosen at random, 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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Bonnie created a website where users could randomly generate a ＂strong password.＂ She claims that

69\%

of generated passwords contain at least one capital letter, number, and symbol.

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If the claim is correct, and a user randomly generates

2

passwords on the website, what is the probability that

0

of the passwords contain at least one capital letter, number, and symbol?

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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.

\newline

If security guards at the festival randomly select

2

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

2

of the tickets are legitimate?

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Write your answer as a decimal rounded 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

9

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

3 / 7

. What is the probability that it will rain on exactly zero of the five days they are there? 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

1 / 6

, what is the probability that the Islanders will win exactly five out of six games in a series against the Rangers? Round your answer to the nearest thousandth.

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If a fair coin is tossed

7

times, what is the probability, to the nearest thousandth, of getting exactly

5

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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

31 \%

. What is the probability that it will rain on exactly three of the four days they are there? 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

7 / 8

. If they have five children, what is the probability that exactly three of their five children will have that trait? Round your answer to the nearest thousandth.

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During a single day at radio station WMZH, the probability that a particular song is played is

0

25

. What is the probability that this song will be played on exactly

6

6

days? Round your answer to the nearest thousandth.

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During a single day at radio station WMZH, the probability that a particular song is played is

0

68

. What is the probability that this song will be played on exactly

2

5

days? Round your answer to the nearest thousandth.

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During a single day at radio station WMZH, the probability that a particular song is played is

1 / 6

. What is the probability that this song will be played on exactly

3

4

days? 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

0

64

. What is the probability that it will rain on exactly one of the six days they are there? Round your answer to the nearest thousandth.

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During a single day at radio station WMZH, the probability that a particular song is played is

2 / 3

. What is the probability that this song will be played on exactly

2

5

days? Round your answer to the nearest thousandth.

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If a fair die is rolled

7

times, what is the probability, rounded to the nearest thousandth, of getting at most

1

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If a fair die is rolled

6

times, what is the probability, rounded to the nearest thousandth, of getting at most

1

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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

64 \%

. What is the probability that it will rain on at most two of the six days they are there? Round your answer to the nearest thousandth.

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During a single day at radio station WMZH, the probability that a particular song is played is

0

52

. What is the probability that this song will be played on at least

5

7

days? 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

5 / 6

. What is the probability that it will rain on at least five of the seven days they are there? 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

67 \%

, what is the probability that the Islanders will win at least four out of seven games in a series against the Rangers? Round your answer to the nearest thousandth.

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If a fair coin is tossed

9

times, what is the probability, rounded to the nearest thousandth, of getting at least

7

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During a single day at radio station WMZH, the probability that a particular song is played is

1 / 3

. What is the probability that this song will be played on at most

2

4

days? 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

48

. If they have four children, what is the probability that at most two of their four children will have that trait? Round your answer to the nearest thousandth.

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If a fair coin is tossed

7

times, what is the probability, rounded to the nearest thousandth, of getting at most

1

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