All categories

3 years ago

A group of 30 people, 12 females and 18 males, are electing 5 representatives.

Mathematics

1 answer:

Alekssandra [29.7K]3 years ago

4 0

Answer:

Total number = 30
Number of females = 12
Number of males = 18

a) Combination of 5 out of 30:

30C5 = 30!/[5!*(30 - 5)!] = 142506

b) Combination of 2 males:

18C2 = 18!/[2!*(18 - 2)!] = 153

Combination of 3 females:

12C3 = 12!/[3!*(12 - 3)!] = 220

The number of ways with 2 males and 3 females:

153*220 = 33660

c) Required probability is:

P(2 males and 3 females) = 33660 / 142506 = 0.236

You might be interested in

Jim is 3 times as old as his cousin Anthony the difference in their age is 18.How old is Jim?

IgorC [24]

Let's create expressions and equations to model this situation. Let Anthony's age be a.

"Jim is 3 times as old as his cousin, Anthony." Jim's age is 3a.
"The difference in their age is 18." 3a - a = 18

How old is Jim?

Let's solve the above equation for a to first find Anthony's age.

3a - a = 18
2a = 18
a = 9

Remember, Jim's age is represented by the expression 3a. Substitute Anthony's age, 9, into the expression to find Jim's age.

3a
3(9)
27

Answer:
Jim is 27 years old.

6 0

2 years ago

Find the difference between the polynomials:–3x+x3–2x2 and 4x3–2x2–4x

allsm [11]

Answer:

x-3x^3

Step-by-step explanation:

^ means to the power of btw

5 0

3 years ago

Mitt is a quality control inspector for a local factory. In today's inspection, Mitt found 5 defective light bulbs out of 60 ins

Otrada [13]

Answer:hahahha

Step-by-step explanation:

Ima just type to get points lol

3 0

2 years ago

All values of x 5 ( x + 10 )^2 − 30 = − 5 Plzzzz

Sedaia [141]

I got -7. 76 or rounded to -8. If right can you please mark me brainliest?

6 0

3 years ago

According to a study done by a university student, the probability a randomly selected individual will not cover his or her mou

Sergio [31]

Using the binomial distribution, it is found that:

a) There is a 0.1618 = 16.18% probability that among 18 randomly observed individuals exactly 6 do not cover their mouth when sneezing.

b) There is a 0.104 = 10.4% probability that among 18 randomly observed individuals fewer than 3 do not cover their mouth when sneezing.

c) 9 is more than 2.5 standard deviations below the mean, hence it would not be surprising if fewer than half covered their mouth when sneezing.

<h3>What is the binomial distribution formula?</h3>

The formula is:

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

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

The parameters are:

x is the number of successes.

n is the number of trials.

p is the probability of a success on a single trial.

The values of the parameters are given as follows:

n = 18, p = 0.267.

Item a:

The probability is P(X = 6), hence:

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 6) = C_{18,6}.(0.267)^{6}.(0.733)^{12} = 0.1618$

There is a 0.1618 = 16.18% probability that among 18 randomly observed individuals exactly 6 do not cover their mouth when sneezing.

Item b:

The probability is:

P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2).

Then:

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 0) = C_{18,0}.(0.267)^{0}.(0.733)^{18} = 0.0037$

$P(X = 1) = C_{18,1}.(0.267)^{1}.(0.733)^{17} = 0.0245$

$P(X = 2) = C_{18,2}.(0.267)^{2}.(0.733)^{16} = 0.0758$

P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0.0037 + 0.0245 + 0.0758 = 0.104.

There is a 0.104 = 10.4% probability that among 18 randomly observed individuals fewer than 3 do not cover their mouth when sneezing.

item c:

We have to look at the mean and the standard deviation, given, respectively, by:

E(X) = np = 18 x 0.267 = 4.81.

$\sqrt{V(X)} = \sqrt{18(0.267)(0.733)} = 1.88$

9 is more than 2.5 standard deviations below the mean, hence it would not be surprising if fewer than half covered their mouth when sneezing.

More can be learned about the binomial distribution at brainly.com/question/24863377

#SPJ1

6 0

2 years ago