Mathematics, 02.04.2020 02:04 FortniteB

A foreign student club lists as its members 2 Canadians, 3 Japanese, 5 Italians, and 2 Germans. If a committee of 4 is selected at random, ﬁnd the probability that (a) all nationalities are represented; (b) all nationalities except Italian are represented

Answers: 3

Show answers

Answers

Answer from: earthangel456

A) The probability that all nationalities are represented is 0.5%.

B) The probability that all nationalities except Italian are represented is 7%.

Given that a foreign student club lists as its members 2 Canadians, 3 Japanese, 5 Italians, and 2 Germans, if a committee of 4 is selected at random, to ﬁ nd the probability that (A) all nationalities are represented; (B) all nationalities except Italian are represented; the following calculations must be performed:

2 + 3 + 5 + 2 = 12

2/12 x 3/11 x 5/10 x 2/9 = X 0.0050 = X 0.0050 x 100 = 0.5

Therefore, the probability that all nationalities are represented is 0.5%.

7/12 x 6/11 x 5/10 x 4/9 = X 0.070 = X 0.070 x 100 = 7

In turn, the probability that all nationalities except Italian are represented is 7%.

Learn more in link

Answer from: stankyweezle

(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.

Answer from: Quest

Idon’t get what to wear lol i ok i’m so sorry but whatever lol omg was my mom like

Answer from: Quest

step-by-step explanation:

divide 13.5 by 9 to get the scale factor. it equals 1.5

2 * 1.5 = 3

Can someone plz answer this for me? whoever answers it first, i will give !

Another question on Mathematics

Mathematics, 21.06.2019 16:00

Apatient is to take 60 mg of an antibiotic on day 1, take 45mg on days 2 and 3, take 30mg on days 4 and 5 and take 15 mg on days 6 and 7. how many total mg will the patient take?

Answers: 1

Answer

Mathematics, 21.06.2019 17:30

Simplify this expression.2(10) + 2(x – 4) a. 2x + 16 b. x + 12 c. 2x + 12 d. x + 16

Answers: 2

Answer

Mathematics, 22.06.2019 01:00

Asmall book publisher knows that 26 books weigh 41 lbs. how much do 40 books weigh?

Answers: 1

Answer

Mathematics, 22.06.2019 01:00

Which is an accurate comparison of the two data sets? the commute to work is typically shorter and more consistent than the commute home. the commute to work is typically shorter but less consistent than the commute home. the commute to work is typically longer and less consistent than the commute home. the commute to work is typically longer but more consistent than the commute home.

Answers: 2

Answer

You know the right answer?

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

Questions