In the United States, voters who are neither Democrat nor Republican are called

(A)
Obtain the probability that none of the people are Independent.
The probability that none of the people are Independent is obtained below as follows:
Let X denote the number of people are independent which follows binomial distribution with the probability 0.10 and the random number of people selected is 30. That is, $X~B\left(30,0.10\right)$
The probability distribution is given by,
$P\left(X=x\right)=\left(\begin{array}{c}n\\ x\end{array}\right)p^x{\left(1-p\right)}^{n-x}$; here $x=0,1,2,\dots ,n$ for $0\le p\le 1$
Where 7 is the number of trials and
p is the probability of success for each trial.
Use Excel to obtain the probability value for x equals 0.
Follow the instruction to obtain the P-value:
1. Open EXCEL
2. Go to Formula bar.
3. In formula bar enter the function as“=BINOMDIST”
4. Enter the number of success as 0.
5. Enter the Trails as 30.
6. Enter the probability as 0.10
7. Enter the cumulative as False.
8. Click enter.
EXCEL output:
From the Excel output, the P-value is 0.0424,
The probability that none of the people are Independent is 0.0424.

(B)
Obtain the probability that fewer than 5 are Independent.
The probability that fewer than 5 are Independents obtained below as follows:
The required probability is,
$P\left(X<5\right)=P\left(X\le 4\right)$
Use Excel to obtain the probability value for x equals 4.
Follow the instruction to obtain the P-value:
1. Open EXCEL
2. Go to Formula bar.
3. In formula bar enter the function as“=BINOMDIST”
4. Enter the number of success as 4.
5. Enter the Trails as 30.
6. Enter the probability as 0.10
7. Enter the cumulative as True.
8. Click enter.
EXCEL output:
From the Excel output, the P-value is 0.8245,
The probability that fewer than 5 are Independent is 0.8245.

(C)
Find the likelihood that there are more than two independent individuals.
The following calculation gives the likelihood that there are more than two independent parties:
The required probability is,
$P(X>2)=1-P(X\le 2)$
Use Excel to obtain the probability value for x equals 2.
Follow the instruction to obtain the P-value:
1. Open EXCEL
2. Go to Formula bar.
3. In formula bar enter the function as"=BINOMDIST”
4. Enter the number of success as 2.
5. Enter the Trails as 30.
6. Enter the probability as 0.10
7. Enter the cumulative as True.
8. Click enter.
EXCEL output:
From the Excel output, the P-value is 0.4114
Therefore,
$P(X>2)=1-P(X\le 2)$
$=1-0.4114$
$=0.5886$
The likelihood that there are more than two Independents is 0.5886.