Math Problem Statement

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 15 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 6 are Independent?

Probability =

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

Probability =

Solution

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Math Problem Analysis

Mathematical Concepts

Probability
Binomial Distribution
Cumulative Probability

Formulas

Binomial Probability Formula: P(X = k) = C(n, k) * p^k * (1 - p)^(n-k)
Cumulative Probability: P(X < k) = Sum(P(X = i) for i = 0 to k-1)
Complement Rule: P(X > k) = 1 - P(X ≤ k)

Theorems

Binomial Theorem
Law of Total Probability

Suitable Grade Level

Grades 9-12