Answer:
The probability is 0.152
Step-by-step explanation:
We know that in this town 39% of all voters are Democrats. Therefore, the probability of a randomly selected voter being a Democrat is [tex]p=0.39[/tex]
The experiment of randomly select voters for a survey is called a Bernoulli experiment (under some suppositions). We suppose that exist independence in this randomly selection of voters. We also suppose that there are only two possibilities for the voter : It is Democrat or not.
Now the variable X : ''The randomly selected voter for a survey is Democrat'' is a Binomial random variable.
X ~ Bi (n,p)
The probability function for the BInomial random variable X is :
[tex]P(X=x)=(nCx).p^{x}.(1-p)^{n-x}[/tex]
Where ''n'' is the number of Bernoulli experiments (In this case n = 2 because we randomly selected two voters)
P(X=x) is the probability of the variable X to assumes the value x
(nCx) is the combinatorial number define as
[tex](nCx)=\frac{n!}{x!(n-x)!}[/tex]
p = 0.39 in this exercise.
We are looking for P(X=2) ⇒
[tex]P(X=2)=(2C2).(0.39)^{2}.(1-0.39)^{2-2}=(0.39)^{2}=0.1521[/tex]
If we round to the nearest thousandth the probability is 0.152
