Math Problem Statement

Based on a​ survey,

3838​%

of likely voters would be willing to vote by internet instead of the​ in-person traditional method of voting. For each of the​ following, assume that

1414

likely voters are randomly selected. Complete parts​ (a) through​ (c) below.

Question content area bottom

Part 1

a. What is the probability that exactly

1111

of those selected would do internet​ voting?

In a binomial probability​ distribution, probabilities can be calculated by using​ technology, a table of binomial​ probabilities, or the binomial probability​ formula, shown below where n is the number of​ trials, x is the number of successes among n​ trials, p is the probability of success in any one​ trial, and q is the probability of failure in any one trial

​(qequals=1minus−​p).

​P(x)equals=StartFraction n exclamation mark Over left parenthesis n minus x right parenthesis exclamation mark x exclamation mark EndFraction times p Superscript x Baseline times left parenthesis 1 minus p right parenthesis Superscript n minus xn!(n−x)!x!•px•(1−p)n−x​,

for

xequals=​0,

​1, 2,​ ..., n

While either technology or the binomial probability formula can be used to find the simple binomial​ probabilities, for this​ exercise, use technology.

Solution

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Math Problem Analysis

Mathematical Concepts

Probability
Binomial Distribution

Formulas

P(x = k) = C(n, k) * p^k * (1 - p)^(n - k)
C(n, k) = n! / [k!(n - k)!]

Theorems

Binomial Theorem

Suitable Grade Level

Grades 10-12