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Alona [7]
3 years ago
8

An urn contains ten chips. An unknown number of chips are white' the others are red. We wish to test:

Mathematics
1 answer:
Olin [163]3 years ago
5 0

Answer:

Let’s denote X to be the number of white chips in the sample and E be the event that exactly half of the chips  are white. Then,

a) Find α

α = P (reject H0 | H0 is true) = P (X ≥ 2|E)  

  = P (X = 2|E) + P (X = 3|E),    

We took two case, as we can draw only only three chips with two or more white to reject H0, it means we can only take 2 white chips or 3, not more, we get solution

  =  (5C2 * 5C1)/10C3  +  (5C3 * 5C0)/10C3

  =  0.5

So,  α = 0.5

b) Find β

i) Let E1 be the event that the urn contains 6 white and 4 red chips. (As given)

β = P (accept H0 | E1) = P (X ≤ 1|E1)

  =  (6C0 * 4C3)/10C3  +  (6C1 * 4C2)/10C3

 = 1/3

 = 0.333

So, β = 0.333

i) Let E2 be the event that the urn contains 7 white and 3 red chips. (As given)

β = P (accept H0 | E2) = P (X ≤ 1|E2)

  =  (7C0 * 3C3)/10C3  +  (7C1 * 3C2)/10C3

 = 11/60

 = 0.183

So, β = 0.183

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3 years ago
You take a three-question true or false quiz. You guess on all the questions. What is the probability that you will get a perfec
elena-14-01-66 [18.8K]
The probability that you will guess the first answer correctly  =  1/2  =  0.5
The probability that you will guess the second answer correctly  =  1/2  =  0.5
The probability that you will guess the third answer correctly  =  1/2  =  0.5

The probability that you will guess all three answers correctly is

                (0.5) x (0.5) x (0.5)  =  0.125  =  12.5% .

============================

Here are all the ways your answer sheet could wind up:
(R = a right answer.  W = a wrong answer.)

W W W 
W W R
W R W
W R R
R W W
R W R
R R W
R R R

Number of possible ways to score 0 right out of 3 questions:  1 way
Number of possible ways to score 1 right out of 3 questions:  3 ways
Number of possible ways to score 2 right out of 3 questions:  3 ways
Number of possible ways to score 3 right out of 3 questions:  1 way

Statistically, if your answers are all pure guesses, 
then on the average, the score you expect is

      (0 + 33-1/3 + 33-1/3 + 33-1/3 + 66-2/3 + 66-2/3 + 66-2/3 + 100) / 8

   =                  400 / 8

   =                      50%  .  

If you're happy with that score, great !  
Go to the movies the night before the test,
and start guessing.


5 0
2 years ago
Write in slope intercept form an equation of the line that passes through (-2,5),(-1,1)
Juliette [100K]

Answer:

y=-4x-3

Step-by-step explanation:

Hi there!

We are given the following two points: (-2,5) and (-1,1)

We want to write the equation of the line that passes through these two lines in slope-intercept form

Slope-intercept form is given as y=mx+b, where m is the slope and b is the y intercept

First, let's find the slope

The formula for the slope (m) calculated from 2 points is \frac{y_2-y_1}{x_2-x_1}, where (x_1, y_1) and (x_2, y_2) are points

We have everything we need to calculate the slope, but let's label the value of the points to avoid any confusion

x_1=-2\\y_1=5\\x_2=-1\\y_2=1

Now substitute into the formula

m=\frac{y_2-y_1}{x_2-x_1}

m=\frac{1-5}{-1--2}
Simplify

m=\frac{1-5}{-1+2}

Subtract

m=\frac{-4}{1}

Divide

m=-4

Now substitute -4 as m into the equation:

y=-4x+b

Now we need to find b

As the equation passes through both (-2, 5) and (-1, 1), we can use either point to help solve for b.

Taking (-2,5) for example:

Substitute -2 as x and 5 as y:

5=-4(-2)+b

Multiply

5=8+b

Subtract 8 from both sides

-3=b

Substitute -3 as b.

y=-4x-3

Hope this helps!

See more on this topic here: brainly.com/question/27304092

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kotegsom [21]

Answer:

-6=2/3*-6

Step-by-step explanation:

y=mx+b

slope = m b=y intercept

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