Am I able to get help with this? I kept trying and I'm not getting it.

Question

In the United States, voters who are neither Democrat nor Republican are called Independent. It is believed that 11% of voters are Independent. A survey asked 35 people to identify themselves as Democrat, Republican, or Independent.

A. What is the probability that none of the people are Independent?

Probability = 

B. What is the probability that fewer than 5 are Independent?

Probability = 

C. What is the probability that more than 2 people are Independent?

Probability = 

Answer 1

Independent = neither Democrat nor Republican

P(Independent) = 0.11

n = 35 people surveyed

a.) Complement Rule: P(not Independent) = 1 - P(Independent) = 1 - 0.11 = 0.89

The probability that none of the people are Independent is 0.89.

b.) Use the binomial probability formula to find the probability that fewer than 5 people are Independent.

P(X = x) = C(35, x) * (0.11)^x * (0.89)^{35 - x} , where x is the number of people selected who are Independent.

P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) = 0.6601

The probability that fewer than 5 people who are Independent is about 0.6601.

c.) Complement Rule: P(X > 2) = 1 - P(X ≤ 2) = 1 - [P(X = 0) + P(X = 1) + P(X = 2)] = 1 - 0.244 = 0.756

The probability that more than 2 people who are Independent is about 0.756.