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2 years ago

Guys, please help me with this question I'm having trouble in solving this

Mathematics

1 answer:

navik [9.2K]2 years ago

6 0

C I think okay bye now

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A foreign student club lists as its members 2 Canadians, 3 Japanese, 5 Italians, and 2 Germans. If a committee of 4 is selected

Fittoniya [83]

Answer:

(a) The probability that the members of the committee are chosen from all nationalities $=\frac{4}{33}$ =0.1212.

(b)The probability that all nationalities except Italian are represent is 0.04848.

Step-by-step explanation:

Hypergeometric Distribution:

Let $x_1$ , $x_2$ , $x_3$ and $x_4$ be four given positive integers and let $x_1+x_2+x_3+x_4= N$ .

A random variable X is said to have hypergeometric distribution with parameter $x_1$ , $x_2$ , $x_3$ , $x_4$ and n.

The probability mass function

$f(x_1,x_2.x_3,x_4;a_1,a_2,a_3,a_4;N,n)=\frac{\left(\begin{array}{c}x_1\\a_1\end{array}\right)\left(\begin{array}{c}x_2\\a_2\end{array}\right) \left(\begin{array}{c}x_3\\a_3\end{array}\right) \left(\begin{array}{c}x_4\\a_4\end{array}\right) }{\left(\begin{array}{c}N\\n\end{array}\right) }$

Here $a_1+a_2+a_3+a_4=n$

${\left(\begin{array}{c}x_1\\a_1\end{array}\right)=^{x_1}C_{a_1}= \frac{x_1!}{a_1!(x_1-a_1)!}$

Given that, a foreign club is made of 2 Canadian members, 3 Japanese members, 5 Italian members and 2 Germans members.

$x_1$ =2, $x_2$ =3, $x_3$ =5 and $x_4$ =2.

A committee is made of 4 member.

N=4

(a)

We need to find out the probability that the members of the committee are chosen from all nationalities.

$a_1$ =1, $a_2$ =1, $a_3$ =1 , $a_4$ =1, n=4

The required probability is

$=\frac{\left(\begin{array}{c}2\\1\end{array}\right)\left(\begin{array}{c}3\\1\end{array}\right) \left(\begin{array}{c}5\\1\end{array}\right) \left(\begin{array}{c}2\\1\end{array}\right) }{\left(\begin{array}{c}12\\4\end{array}\right) }$

$=\frac{2\times 3\times 5\times 2}{495}$

$=\frac{4}{33}$

=0.1212

(b)

Now we find out the probability that all nationalities except Italian.

So, we need to find out,

$P(a_1=2,a_2=1,a_3=0,a_4=1)+P(a_1=1,a_2=2,a_3=0,a_4=1)+P(a_1=1,a_2=1,a_3=0,a_4=2)$

$=\frac{\left(\begin{array}{c}2\\2\end{array}\right)\left(\begin{array}{c}3\\1\end{array}\right) \left(\begin{array}{c}5\\0\end{array}\right) \left(\begin{array}{c}2\\1\end{array}\right) }{\left(\begin{array}{c}12\\4\end{array}\right) }+\frac{\left(\begin{array}{c}2\\1\end{array}\right)\left(\begin{array}{c}3\\2\end{array}\right) \left(\begin{array}{c}5\\0\end{array}\right) \left(\begin{array}{c}2\\1\end{array}\right) }{\left(\begin{array}{c}12\\4\end{array}\right) }$ $+\frac{\left(\begin{array}{c}2\\1\end{array}\right)\left(\begin{array}{c}3\\1\end{array}\right) \left(\begin{array}{c}5\\0\end{array}\right) \left(\begin{array}{c}2\\2\end{array}\right) }{\left(\begin{array}{c}12\\4\end{array}\right) }$

$=\frac{1\times 3\times 1\times 2}{495}+\frac{2\times 3\times 1\times 2}{495}+\frac{2\times 3\times 1\times 1}{495}$

$=\frac{6+12+6}{495}$

$=\frac{8}{165}$

=0.04848

The probability that all nationalities except Italian are represent is 0.04848.

6 0

3 years ago

tickets for a lower level seats sell for $35 each and tickets for an upper level seats sell for $25 each. the theater sells 350

Liono4ka [1.6K]

The work and answer is shown in the image below. Just set the variables and solve.

5 0

2 years ago

Determine the Cartesian coordinates of the points with polar coordinates (\sqrt{2}, \pi/4 ), (0, \pi), (-1,400\pi), and ( 2\sqrt

yarga [219]

Answer:

Step-by-step explanation:

We have the conversion from polar coordinates to cartesian as

x =rcost and y = rsint where (r,t) are the polar coordinates

Also all trignometric functions are periodic with period = 2pi

Using this we find out

$(\sqrt{2}, \pi/4 ) = (\sqrt{2}cos \pi/4, \sqrt{2}cos \pi/4,)=(1,1)\\ (0, \pi), (-1,400\pi),=(0 cos 1400 \pi, 0 sin 1400\pi)\\= (0, 0)\\\\ ( 2\sqrt{3},- 2\pi / 3) = (2\sqrt{3}, cos2\pi / 3, 2\sqrt{3},sin2\pi / 3))\\=(-\sqrt{3}, 3)$

Thus we converted polar to rectangular coordinates.

Reverse would be

from (x,y) to (r,t) as

$r=\sqrt{x^2+y^2} \\tant = y/x$

8 0

3 years ago

If james had seven dollars and ruby had 3,963,927 dollars. what is the sum divided by 286 times 74 subtracted then timed by 7 to

valkas [14]

Answer:

Step-by-step explanation:

ok lets do thiiiiis

7+3963927 / 286 * 74 - 7^6 * 7^6

. first start with the exponets.

7+ 3963927 / 286 * 74 - 117649 * 117649

multiplication is next 286 * 74

now we got 7+ 3963927 / 21,164 - 13841287201 do the math and your left with

3963934 / 138141266037

3 0

3 years ago

Read 2 more answers

1.Do you think a similar rule is true for cosine? That is, does –cos(θ) = cos(–θ)? Pick a value of θ and test this theory.

adell [148]

1.Do you think a similar rule is true for cosine? That is, does -cos (θ) = cos (-θ)? Pick a value of θ and test this theory.

It is not the same.
To prove it, let's choose a value of the angle:
θ = 45 degrees:
-cos (θ) = cos (-θ)
-cos (45) = cos (-45)
- (root (2) / 2) = (root (2) / 2)
answer:
NOT fulfilled: -cos (θ) = cos (-θ) (false)

2. Using your example above, speculate on a rule that might be true for cos (-θ).
cos (θ) = cos (-θ)
To prove it, let's choose a value of the angle:
θ = 45 degrees:
cos (θ) = cos (-θ)
cos (45) = cos (-45)
(root (2) / 2) = (root (2) / 2)
answer
A rule for cosine can be:
cos (θ) = cos (-θ)

7 0

2 years ago