In one town, 39% of all voters are democrats. if two voters are randomly selected for a survey, find the probability that they are both democrats. round to the nearest thousandth if necessary.

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

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 :

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

p = 0.39 in this exercise.

We are looking for P(X=2) ⇒

If we round to the nearest thousandth the probability is 0.152

d) by the cross product property, ab^2 = bc multiplied by ad

step-by-step explanation:

we are given

in the given triangle abc

angle a is 90° and segment ad is perpendicular to segment bc

we can see that

triangle(abc) and triangle(abd) are similar because they have common side and same angle (90 degree)

so, triangles(abc) and abd are similar

since, they are similar

so, the ratio of their sides must be equal

we get

now, we can cross multiply

and we get

so, this could be step to prove it