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allsm [11]
2 years ago
6

A bin of 50 manufactured parts contains 3 defective parts and 47 non-defective parts. A sample of size 6 parts is selected from

50 parts. Selected parts are not replaced. How many different samples are there of size six that contain exactly 2 defective parts? What is the probability that a sample contains exactly 2 defective parts?
Mathematics
1 answer:
lyudmila [28]2 years ago
8 0

Answer:

535,095 different samples of size six that contain exactly 2 defective parts.

0.0337 = 3.37% probability that a sample contains exactly 2 defective parts.

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

As the order of the parts is not important, the combinations formula is used to solve this question.

Combinations formula:

C_{n,x} is the number of different combinations of x objects from a set of n elements, given by the following formula.

C_{n,x} = \frac{n!}{x!(n-x)!}

How many different samples are there of size six that contain exactly 2 defective parts?

2 defective from a set of 3, and 4 non-defective from a set of 47. So

D = C_{3,2}*C_{47,4} = \frac{3!}{2!1!}*\frac{47!}{4!43!} = 535095

535,095 different samples of size six that contain exactly 2 defective parts.

What is the probability that a sample contains exactly 2 defective parts?

The total number of samples is:

T = C_{50,6} = \frac{50!}{6!44!} = 15890700

Then...

p = \frac{D}{T} = \frac{535095}{15890700} = 0.0337

0.0337 = 3.37% probability that a sample contains exactly 2 defective parts.

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5 0
3 years ago
Arrange the circles (represented by their equations in general form) in ascending order of their radius lengths. X2 y2 − 2x 2y −
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Circles (represented by their equations in general form) in ascending order of their radius lengths can be arranged as first-fifth-second-forth-third-seventh-sixth.

<h3>What is the equation of circle?</h3>

The equation of the circle is the equation which is used to represent the circle in the algebraic equation form with the value of center point in the coordinate plane and measure of radius.

The standard form of the equation of the circle can be given as,

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The radius of this circle is √(3).

Lets arrange the second equation, in standard form of equation of circle as,

x^2 +y^2 - 4x+ 4y - 10 = 0  \\(x^2 - 4x) +(y^2+ 4y )= 10\\(x^2 - 4x+4) +(y^2+ 4y +4)= 10+4+4\\(x-2)^2+(y+2)^2=(\sqrt{18})^2

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The radius of this circle is √(45).

Similarly, radius of the forth, fifth, sixth and seventh circle is √(23), √(5), √(117) and √(46) units.

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Learn more about the equation of circle here;

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✧・゚: *✧・゚:*    *:・゚✧*:・゚✧

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✧・゚: *✧・゚:*    *:・゚✧*:・゚✧

❖ The area of the square is 25 square inches.

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~ ʜᴏᴘᴇ ᴛʜɪꜱ ʜᴇʟᴘꜱ! :) ♡

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First choice


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3 years ago
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