MATHEMATICS COLLEGE

A bag contains 6 red marbles, 3 blue marbles and 7 green marbles. If three marblesare drawn out of the bag, what is the probability, to the nearest 1000th, that all three
marbles drawn will be red?

Answers

Answer 1

Answer:

Answer: 0.036

Work Shown:

6 red, 6+3+7 = 16 total

A = 6/16 = probability of getting red the first time

after you pick 1 red, there's 6-1 = 5 left out of 16-1 = 15 total

B = 5/15 = probability of getting red the second time

then you repeat: 5-1 = 4 red left out of 15-1 = 14 total

C = 4/14 = probability of getting red the third time

B and C are dependent on A, C is dependent on B. This is assuming we do not put any marbles back.

Multiply out the fractions found

A*B*C = (6/16)*(5/15)*(4/14) = 0.0357 which rounds to 0.036 when rounding to the nearest thousandth.

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An airline company is considering a new policy of booking as many as 354 persons on an airplane that can seat only 330. (Past studies have revealed that only 88% of the booked passengers actually arrive for the flight.) Estimate the probability that if the company books 354 persons, not enough seats will be available

Answers

Title:

See the explanation.

Step-by-step explanation:

It is given that, if 100 persons book their seats, then only 88 passengers come.

The probability of 1 passenger to come is $(88)/(100)$ = 0.88.

There will not be enough seats only when, 331 or more than 331 passengers will come.

The probability of 1 passenger will not come is (1 - 0.88)= 0.12.

Out of 354 passengers the probability that n passengers will come is $^(354)C_n (0.88)^n (0.12)^(354 - n)$ .

The required probability is ∑ $^(354)C_n (0.88)^n (0.12)^(354 - n)$ , where $331\leq n \leq 354$ .

A teacher recorded the time, in minutes, it took each student in two classes to complete a quiz. The results are shown in the box plots below.

Answers

|||||||||Where?|||||||||||||

???? Where is the box plot?????

Derive cos (2x - 1)

Answers

Answer:

Step-by-step explanation:

I believe that what you want to do here is to "differentiate" cos (2x - 1).

We must use the rule for differentiating cos x and also the chain rule, since the input to cos x here is (2x - 1).

(d/dx) is the derivative operator.

(d/dx) (cos x) = -sin x

(d/dx) cos (2x - 1) = - sin (2x - 1) * (d/dx) (2x -1) = -sin (2x - 1)(2) = -2sin (2x - 1)

Which of the following groups have terms that can be used interchangeably?a. critical value, probability, proportion
b. percentage, probability, proportion
c. critical value, percentage, proportion
d. critical value, percentage, probability

Answers

percentage, probability, proportion are all very similar terms (not 100% identical but closely related)

The answer is choice B

Blood potassium level, continued. Judy’s measured potassium level varies according to the Normal distribution with with μ=3.8 and σ=0.2mmol/l. Let’s consider what could happen if we took 4 separate measurements from Judy. What is the blood potassium level L such that the probability is only 0.05 that the average of 4 measurements is less than L? (Hint: This requires a backward Normal calculation.)the book says about 3.64 but i got 3.28

Answers

Answer:

The value of l = 3.64

Step-by-step explanation:

Consider the provided information.

μ=3.8 and σ=0.2mmol/l and n=4

As we know $\mu_(\bar x)=\mu=3.8$

$\sigma_(\bar x)=(\sigma)/(√(n))=(0.2)/(√(4))=0.1$

We have given α = 0.05

So by the standard normal table: $Z_(0.05)=-1.645$

Compute $P(\bar{X}<l)=0.05$

$P(z<(l-3.8)/(0.1))=0.05$

$(l-3.8)/(0.1)=-1.645$

$l-3.8=-0.1645$

$l=3.64$

Hence, the value of l = 3.64

Sharon and Dani make invitations for a party.Sharon makes 27 invitations. That is 3 times as many as Dani makes.write and solve an equation to find the number of invitations Dani makes