Mathematics, 24.10.2019 08:43, BOYAWESOME0202

In the united states, voters who are neither democrat nor republican are called independent. it is believed that 9% of voters are independent. a survey asked 12 people to identify themselves as democrat, republican, or independent.

a. what is the probability that none of the people are independent?

b. what is the probability that fewer than 6 are independent?

c. what is the probability that more than 3 people are independent?

Answers: 1

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answered: kaymillsaps

Using the binomial distribution, it is found that:

a) 0.3225 = 32.25% probability that none of the people are Independent.

b) 0.9997 = 99.97% probability that fewer than 6 are Independent.

c) 0.018 = 1.8% probability that more than 3 people are Independent.

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For each voter, there are only two possible outcomes. Either they are independent, or they are not. The probability of a voter being independent is independent of any other voter, which means that the binomial distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials.

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

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

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

In this problem:

9% are independent, thus p = 0.09

12 voters, thus n = 12

Item a:

This probability is P(X = 0), thus:

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

$P(X = 0) = C_{12,0}.(0.09)^{0}.(0.91)^{12} = 0.3225$

0.3225 = 32.25% probability that none of the people are Independent.

Item b:

This is:

P(X < 6) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5)

Then

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

$P(X = 0) = C_{12,0}.(0.09)^{0}.(0.91)^{12} = 0.3225$

$P(X = 1) = C_{12,1}.(0.09)^{1}.(0.91)^{11} = 0.3827$

$P(X = 2) = C_{12,2}.(0.09)^{2}.(0.91)^{10} = 0.2082$

$P(X = 3) = C_{12,3}.(0.09)^{3}.(0.91)^{9} = 0.0686$

$P(X = 4) = C_{12,4}.(0.09)^{4}.(0.91)^{8} = 0.0153$

$P(X = 5) = C_{12,5}.(0.09)^{5}.(0.91)^{7} = 0.0024$

P(X < 6) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) = 0.3225 + 0.3827 + 0.2082 + 0.0686 + 0.0153 + 0.0024 = 0.9997

0.9997 = 99.97% probability that fewer than 6 are Independent.

Item c:

This probability is:

$P(X 3) = 1 - P(X \leq 3)$

In which

$P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)$

From item b:

$P(X \leq 3) = 0.3225 + 0.3827 + 0.2082 + 0.0686 = 0.982$

$P(X 3) = 1 - P(X \leq 3) = 1 - 0.982 = 0.018$

0.018 = 1.8% probability that more than 3 people are Independent.

A similar problem is given at link

answered: skaterwolf1317

(a) 0.3225

(b) 0.9997

Step-by-step explanation:

Since 9% of voters are independent, p=0.09 and n=12, the required probability is,

$P(X=0)=\left[\begin{array}{c}12\\0\\\end{array}\right](0.09)^{0}(1-0.09)^{12-0}$ =0.322475487

Therefore, p=0.3225

(b)

Probability that fewer than 6 are independent voters

P(X<6)=[P(X=0)+ P(X=1)+ P(X=2)+ P(X=3)+ P(X=4)+ P(X=5)]

P(X<6)= $(\left[\begin{array}{c}12\\0\\\end{array}\right](0.09)^{0}(1-0.09)^{12-0})+(\left[\begin{array}{c}12\\0\\\end{array}\right](0.09)^{1}(1-0.09)^{12-1})+(\left[\begin{array}{c}12\\0\\\end{array}\right](0.09)^{2}(1-0.09)^{12-2})+(\left[\begin{array}{c}12\\0\\\end{array}\right](0.09)^{3}(1-0.09)^{12-3})+(\left[\begin{array}{c}12\\0\\\end{array}\right](0.09)^{4}(1-0.09)^{12-4})+(\left[\begin{array}{c}12\\0\\\end{array}\right](0.09)^{5}(1-0.09)^{12-5})+(\left[\begin{array}{c}12\\0\\\end{array}\right](0.09)^{6}(1-0.09)^{12-6})$

P(X<6)=0.322475+0.382718161+0.2081819+0.068631+0.01527237+0.00241673= 0.999696

P(X<6)=0.9997

Therefore, probability that fewer than six people are independent is 0.9997

(c)

Probability that more than 3 people are independent voters

P(X>3)=1-P(X≤3)=1-[P(X=0)+P(X=1)+P(X=2)+P(X=3)]

=1-{ $(\left[\begin{array}{c}12\\0\\\end{array}\right](0.09)^{0}(1-0.09)^{12-0})+(\left[\begin{array}{c}12\\0\\\end{array}\right](0.09)^{1}(1-0.09)^{12-1})+(\left[\begin{array}{c}12\\0\\\end{array}\right](0.09)^{2}(1-0.09)^{12-2})+(\left[\begin{array}{c}12\\0\\\end{array}\right](0.09)^{3}(1-0.09)^{12-3})}$

=1-(0.322475+0.382718161+0.2081819+0.068631)

=1-0.982007=0.01799311

P(X>3)= 0.01799

answered: Guest

c. 27 units.

step-by-step explanation:

we are told that in circle a, ∠bae ≅ ∠dae.

we can see from our given diagram that in $\delta bea$ and $\delta dea$ ;

$ba=da$ , as these are radii of our given circle.

$ea=ea$

therefore, $\delta bea\cong \delta dea$ by sas congruence postulate.

hence, side be will be equal to side de as corresponding parts of congruent triangles are congruent. so we can set an equation to find the value of x as:

$3x-24=x+10$

$3x-x=24+10$

$2x=34$

$x=\frac{34}{2}$

$x=17$

now let us substitute x=17 in the expression for the length of be.

$\text{length of be}=3x-24$

$\text{length of be}=3\cdot 17-24$

$\text{length of be}=51-24$

$\text{length of be}=27$

therefore, length of be will be 27 units and option c is the correct choice.

In circle a, ∠bae ≅ ∠dae. what is the length of be? 14 units 17 units 27 units 34 units

answered: Guest

4if you add the absolute values together

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In the united states, voters who are neither democrat nor republican are called independent. it is b...