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AleksAgata [21]
3 years ago
14

A company manufactures plastic eggs, filling each egg with either a prize - a piece of candy -or no prize – a rock. Natasha’s fa

ther buys and hides dozens of the eggs in the garden. Natasha runs out and fills her basket with 10 eggs (the basket is small). Natasha’s father tells her that the manufacturer states that 67 percent of the eggs have a rock inside them. Natasha is the only person searching for eggs.
(A) Is the scenario above a binomial setting, a geometric setting, or neither? Fully justify your response, citing pertinent criteria for your answer.

(B) What is the probability that Natasha’s basket has exactly 7 eggs with rocks?

(C) What is the expected number of eggs with rocks that Natasha will have in her basket?
Mathematics
1 answer:
makvit [3.9K]3 years ago
6 0

Answer:

\red{\underline{\underline{\sf{Answer :-}}}}

There are three characteristics of a binomial experiment. There are a fixed number of trials. Think of trials as repetitions of an experiment. The letter n denotes the number of trials. There are only two possible outcomes, called “success” and “failure,” for each trial. The letter p denotes the probability of a success on one trial, and q denotes the probability of a failure on one trial.

p

+

q

=

1

. The n trials are independent and are repeated using identical conditions. Because the n trials are independent, the outcome of one trial does not help in predicting the outcome of another trial. Another way of saying this is that for each individual trial, the probability, p, of a success and probability, q, of a failure remain the same. For example, randomly guessing at a true-false statistics question has only two outcomes. If a success is guessing correctly, then a failure is guessing incorrectly. Suppose Joe always guesses correctly on any statistics true-false question with probability

p

=

0.6

. Then,

q

=

0.4

. This means that for every true-false statistics question Joe answers, his probability of success

(

p

=

0.6

)

and his probability of failure

(

q

=

0.4

)

remain the same.

The outcomes of a binomial experiment fit a binomial probability distribution. The random variable

X

=

the number of successes obtained in the n independent trials.

The mean,

μ

, and variance,

σ

2

, for the binomial probability distribution are

μ

=

n

p

and

σ

2

=

n

p

q

. The standard deviation,

σ

, is then

σ

=

√

n

p

q

.

Any experiment that has characteristics two and three and where

n

=

1

is called a Bernoulli Trial (named after Jacob Bernoulli who, in the late 1600s, studied them extensively). A binomial experiment takes place when the number of successes is counted in one or more Bernoulli Trials.

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Answer:

The equations are:

4H + 3P = 13.75

2H + 5P = 11.25

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Step-by-step explanation:

Let:

H = hot\ dog

P =Pretzel

For Tina:

4H + 3P = 13.75

For Doug:

2H + 5P = 11.25

Solving for the price of both items:

We have:

4H + 3P = 13.75 --- (1)

2H + 5P = 11.25 --- (2)

Multiply (2) by 2

2 * (2H + 5P = 11.25)

-------------------

4H + 10P = 22.50 --- (3)

Subtract (3) from (1)

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4H + 10P = 22.50

----------------------

4H - 4H + 3P - 10P = 13.75 - 22.50

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Substitute 1.25 for P in (2)

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3 0
2 years ago
Tom is making a rectangular garden. he decides to make the garden 30 ft long by 15 ft wide. Later, tom decides to keep the lengt
OleMash [197]

Yes.  Changing the the word problem into a function, you get 30x=y.

30 = Fixed Length

x = width

y = area

No matter what width (x) you choose, the area (y) is going to be a multiple of 30 (the fixed length) because with two numbers being multiplied, if there is a fixed number that will always be the multiple and not the multiplier.  For example, 10 multiplied by every number 1-10 is going to be a multiple of 10.

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So if Tom chooses any of these widths (x) 5, 10, or 15, y (the area) will be a multiple of 30.

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So as we double 5 to get 10, our outcome is doubled 150 to 300 and so forth.  Hope this helps.

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Hunter-Best [27]

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Quadratic means the highest exponent is 2.

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